chain rule worksheet doc

That is, if f is a function and g is a function, then the chain rule expresses the derivative of the composite function f ∘ g in terms of the derivatives of f and g. Definition •If g is differentiable at x and f is differentiable at g(x), … INTRODUCTION. A find dy dx by implicit di erentiation given that x2 y2 25. We want to derive a rule for the derivative of a composite function of the form in terms of the derivatives of f and g. This rule allows us to differentiate complicated functions in terms of known derivatives of simpler … 39 0 obj <>/Filter/FlateDecode/ID[<9A5A2E3EFDD50B4A85195CB419DC45D6>]/Index[22 35]/Info 21 0 R/Length 85/Prev 34984/Root 23 0 R/Size 57/Type/XRef/W[1 2 1]>>stream Created: Dec 4, 2011. l. Find the derivative of the following functions with respect to the independent variable. Info. Worksheet # 13: Chain Rule 1. g Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Differentiation - Quotient Rule Date_____ Period____ Derivatives of sum, differences, products, and quotients. Power Rule; Exponentials and Logs; Trigonometric Functions; Sum Rule; Product Rule; Quotient Rule; Chain Rule; All Types ; Derivative Worksheets. Mobile Notice. The introduction of each worksheet very brieﬂy summarizes the main ideas but is not intended as a substitute for the textbook or lectures. H��=O1ཿ�FX�$�8� (filled) … Show Mobile Notice Show All Notes Hide All Notes. (b) Suppose f and gare di erentiable functions so that f(2) = 3, f0(2) = 1, g(2) = 1 4, and g0(2) = 2. You appear to be on a device with a "narrow" screen width (i.e. To differentiate this we write u = (x3 + 2), so that y = u2 Students will be able to. •Prove the chain rule •Learn how to use it •Do example problems . The student will be given composite functions and will be asked to differentiate them using the chain rule. It shouldn't take you long to work power rule problems of all types. Target: On completion of this worksheet you should be able to use the chain rule to differentiate functions of a function. Tools for Success-A list of resources including tutoring services. D02 - Chain Rule WS (Kuta).pdf D02-Chain Rule with Polynomials (LP).docx D03-Exponential Derivatives LP.docx D05-Product Rule LP.docx D06-Quotient Rule LP.docx D07-Trigonometric Derivatives LP.docx D08-Advanced Derivatives QUIZ.doc D09-Chain Rule (Day 2) LP.docx D10-Chain Rule (Adv) LP.docx D11-Inverse Trig Derivatives LP.docx 1. log13 (8x3 +8) 2. h�bbd``b`� $�� SL "Dx�� ̛AD=H,D� ��$H\�a`bdX Let . (d) y= xe 2x (e) g(x) = (1 + 4x)5(3 + x x2)8 (f) y= excosx (g) F(z) = Published by Wiley. Chain Rule; Implicit Differentiation; Related Rates; Higher Order Derivatives; Logarithmic Differentiation; Applications of Derivatives. c r TAkl rl 4 Ir xiog3h Dt1sc lr meAsOesr Jvse wda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx =3u2×2=2×3(2x+4)2 dy dx = dy du ⋅ du dx dy dx =6(2x+4)2. 56 0 obj <>stream 2 write y0 dy dx and solve for y 0. Notes - Tangents and Differentiability; Notes - Tangents and Diff. Chain Rule Examples (both methods) doc, 170 KB. Use Chain Rule. Let and (viii) Use Chain Rule. Solution: Here we use the Product Rule along with . Differentiation Using the Chain Rule. Complex Differentiability and Holomorphic Functions Theorem 2.0.1: Let f(z) = u(z) + jv(z) with u(z);v(z) 2R and z= x+ jywith x;y2R. Nearly every multiple‐choice question on differentiation from past released exams uses the Chain Rule. Chain Rule Worksheets. Due to the nature of the mathematics on this site it is best views in landscape mode. 0) = f0(g(z0))g(z0) (chain rule): (2.8) Complex differentiability is closely related to the Cauchy-Riemann equations [Lang, 1993]. View chain_rule_worksheet.doc from MAT MISC at Stony Brook University. Title: Practice Exercise Sheet 1 Author: cwhelan Last modified by: TCD User Created Date: 10/3/2005 3:49:00 PM 1 ln(4x) 17. p ¡cos(x) 18. Example Find d dx (e x3+2). Prev. You appear to be on a device with a "narrow" screen width (i.e. Mobile Notice. The additional problems are more challenging and sometimes deal … 03 - Chain Rule Top cdn.kutasoftware.com ©F f2h0 21D34 0K muFt HaQ DSBo cf DtEw XaErXe2 BLRLYC7. By using the Chain Rule an then the Power Rule, we get = = nu;1 = n*g(x)+;1g’(x) Calculus I Worksheet Chain Rule Find the derivative of each of the following functions. We want to derive a rule for the derivative of a composite function of the form in terms of the derivatives of f … Title: Calculus: Differentiation using the chain rule. ©S w2k0b1 Q3v tKWuFtWai TS Jo nf4t awdakrZet 5LnLsCG.j 4 vA6lOlZ 9rZi 7g HhvtUsK FrecshearQvneUdL.p s NMRaYdAer MwciAtAhN 2I9nCfWian jiatSe y 6CRa JlLcluTl Ju Ast. endstream endobj 26 0 obj <>stream Chain Rule Practice Problems Calculus I, Math 111 Name: 1. Also applies to subtraction in the same way. Problems may contain constants a, b, and c. 1) f (x) = 3x5 f' (x) = 15x4 2) f (x doc, 90 KB. %%EOF No calculator unless othenvise stated. Integration Worksheet - Substitution Method Solutions (a)Let u= 4x 5 (b)Then du= 4 dxor 1 4 du= dx (c)Now substitute Z p 4x 5 dx = Z u 1 4 du = Z 1 4 u1=2 du 1 4 u3=2 2 3 +C = 1 6 !`�$�?�OY��rN "��W�y�w]�� 8��C�F��;" ��A��+H��O�i��Gs�9G��>vA_m�� u#� These Calculus Worksheets will produce problems that involve using the chain rule to differentiate functions. Some of the Worksheets below are Chain Rule Worksheets with Answers, usage of the chain rule to obtain the derivatives of functions, several interesting chain rule exercises with step by step solutions and quizzes with answers, … You may also use any of these materials for practice. Such … pdf doc ; Introduction to Related Rates - Finding various derivatives using volume of a sphere and surface area of a cylinder. FREE (33) SRWhitehouse A level Maths C2: Trig equations worksheets. So we didn’t actually need to go through the last 5 lines. h�b```f``�d`a`�f�c@ >�r`8��[�¢{}s��A�*��"x�nr7O��|@�Q��A}KĢ�< L��p10l��y��C��l �� Find the derivative of the given function. 3 y' = 4 cos2(3.r)cos( 4x) + - 6 sin( 4x) cos( 3x)( sin 3x) 2. Section. Target: On completion of this worksheet you should be able to use the chain rule to differentiate functions of a function. (d) y= xe 2x (e) g(x) = (1 + 4x)5(3 + x x2)8 (f) y= excosx (g) F(z) = Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. 8. That material is here. Derivatives - Power, Product, Quotient and Chain Rule - Functions & Radicals - Calculus Review - Duration: 1:01:58. epwrp)e is Calculus Worksheet Chain Rule Practice #1 Find the derivative of each of the following functions. Differentiation Using the Chain Rule. Some of the worksheets displayed are Chain product quotient rules, Work for ma 113, Product quotient and chain rules, Product rule and quotient rule, Dierentiation quotient rule, Find the derivatives using quotient rule, 03, The product and quotient rules. Showing top 8 worksheets in the category - Chain Rule. Lecture 10: Worksheet The chain rule The rule(f(g(x))0= f0(g(x))g0(x) is called the chain rule. Let (ix) Use Chain Rule. … 3.3 The Chain Rule. Chain Rule Examples Name_ Find f '(x) using the chain rule. Are you working to calculate derivatives using the Chain Rule in Calculus? Updated: Mar 23, 2017. doc, 23 KB. This booklet contains the worksheets for Math 53, U.C. A student will be able to: Know the chain rule and its proof. 6 Ex1b. 5 1. y x 2 4 x 6 2. f ( x) x 3 5 x 11. Derivatives. Need to review Calculating Derivatives that don’t require the Chain Rule? So the derivative of -5(y) 2 is -10y using the power rule, and then the derivative always, . The questions emphasize qualitative issues and the problems are more computationally intensive. Report a problem. 2 Prerequisite: Tutorial on the AcroTEX System of Online Assessment You must enter your answer in the response boxes using a certain “natural” syntax. The following is a list of worksheets and other materials related to Math 122B and 125 at the UA. Solution: We use the Quotient Rule and the natural logarithm rule: Integrals Involving Natural Logarithmic Function. About this resource. Section. Definition •In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. Implicit Differentiation and Related Rates Implicit means “implied or understood though not directly expressed” b) Now find the equation of the line tangent to the curve expressed by at the point (2, -1). Home / Calculus I / Derivatives / Chain Rule. Find the derivatives of the given functions. -�a/��"�sC�&RjC>��,��p-, Worksheet # 13: Chain Rule Worksheet # 14: Implicit Di erentiation and Inverse Functions Worksheet # 15: Related Rates Worksheet # 16: Review for Exam II Worksheet # 17: Linear Approximation and Applications Worksheet # 18: Extreme Values and the Mean Value Theorem Worksheet # 19: The Shape of a Graph Worksheet # 20: Limits at In nity & L’H^opital’s Rule Worksheet # 21: Optimization … Separate the function into its terms and find the derivative of each term. Using L’Hospital’s Rule, take the derivatives of the numerator and denominator twice, to get : ; L Ú. Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the chain rule. View Chain Rule Examples.doc from MATH 225 at Henry Ford College. (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. Date_ Period_ (1) f (x) = sin(3x) (2) f (x) = cos(7x) (3) f (x) = (4x2 + 3 p 4x+9 21. p ¡cos(x) 22. Notes Practice Problems Assignment Problems. For example, the derivative of sin(log(x)) is cos(log(x))=x. HW #12 - Review for 1st Six Weeks Exam ; 1.13: 1st Six Weeks Exam 1.14: Tangents and Differentiability. h z oMxabdJe g EwriZtah l vIJn qfei1nMi2tLe A TC 7a7l qc GuHlruPs 9. b Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Differentiation - Chain Rule … Learning Objectives . Power Rule 1. f(x) = x x3 2. f(x) = 4 x2 x2 4 3. h(x) = 3 p x 4. f(x) = x2 e2 5. g(x) = pp x 6. f(x) = x2 1 x 7. f(x) = 7x+ 3x2 5 p x Chain Rule Find the rst derivative of the following functions: 8. f(x) = (x2 1)10 9. f(x) = p 1 + p 1 + 2x 10. g(x) = (3x2 + 3x 6) 8 11. f(x) = 4 p 9 x Product and Quotient Rule Find the rst derivative of the following functions: 12. f(x) = (x+ 1)(x2 3) (Try this one in two di erent ways.) In the last section, we have learned that the derivative of is . Answer: D Image from the Algebra App available at www.mathguy.us. 10. Worksheet by Kuta Software LLC-4-Chain Rule: 41) y = (x4 - 5) 4 42) y = (-3x3 - 5) 2 43) y = (2x - 1) 3 44) y = (-3x5 - 1) 5 45) y = (-4x2 - 5) 4 46) y = (-x + 4) 2 47) y = ((3x4 + 5) 2 + 5) 4 48) y = ((-x5 + 2) 5 - 5) 2 49) y = ((5x4 + 3) 4 + 1) 2 50) y = ((5x2 - 3) 5 + 2) 4 ©m Z2B0\1e7o YKMuhtfaa USgoafBtjwVadrpel qLqLJCy.m x AANlSll IrDirgsh_tvs_ WrweFshefrdvfeJda.T O ZMDaLdpev owoirtrhv GIxnifdiZnliGttex … Differentiate the following functions: Use rule y = ln x ( (vii) Use the product rule: If , then . Let’s solve some common problems step-by-step so you can learn to solve them routinely for yourself. This section gives a method of differentiating those functions which are what we call composite functions. Derivatives of sum, differences, products, and quotients. Show all files. (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. Simplify your answers and write all exponents as positive exponents! No calculator unless othenvise stated. Worksheet Derivatives Implicit Differentiation Chain Rule Calculus Printable . So the power rule “works” in this case, but it’s really best to just remember that the derivative of any constant function is zero. No calculator unless otherwise stated. pdf doc ; Base e - Derivation of e using derivatives. One. Exercises 3.1. Practice is the best way to improve. Notes Practice Problems Assignment Problems. The power rule combined with the Chain Rule •This is a special case of the Chain Rule, where the outer function f is a power function. 6 2. The Organic Chemistry Tutor 1,090,721 views A student will be able to: Know the chain rule and its proof. l. Find the derivative of the following functions with respect to the independent variable. ��ࡱ� > �� E G �� D � T �� U@ �� S bjbj�� .v �� 1 �� b b b b B B B V �" �" �" 8 �" �# T V �I 2 J$ �. Differentiation Using the Chain Rule. y = x3 + 2 is a function of x y = (x3 + 2)2 is a function (the square) of the function (x3 + 2) of x. ©C N2S0c1h3 j dKJu ntva P zS7oIf ktdweaNrdeR nLQLJC N.y a ZA 0l uln Mrli tg Qhft fs S pr be4s Hehrev Pe2d B.k j WM1a0det 4wti Ctlh2 CInMf8iKnli Vt Zer qC naKlsc DuKlGurs L.e Worksheet by Kuta Software LLC Calculus ©s 92B0 T1 F34 QKZuut4a 8 RS Cohf gtzw baorFe A CLtLhC Q. P L YA0l hlA 2rJiJgHh Bt9s q Pr9eGszecrqv Revd e.2 Chain Rule Practice • The chain rule • Questions 2. Then add up the derivatives. chain rule and implicit differentiation worksheet answers.implicit differentiation examples.implicit differentiation xy.implicit differentiation worksheet doc.implicit differentiation calculator.implicit differentiation steps.implicit differentiation word problems.implicit differentiation worksheet doc.hardest derivative problem.implicit differentiation quotient rule.logarithmic differentiation … Of a cylinder Hospital ’ s rule, and then the derivative of -5 ( y ) 2 -10y! Solve them routinely for yourself we have learned that the derivative of a cylinder, 23.. Doc ; Base e - Derivation of e using derivatives due to the of... 4 x 6 2. f ( x ) ) is cos ( log ( x 15....: Integration worksheets along with: Mar 23, 2017. doc, 170 KB simplify! Exam 1.14: Tangents and Diff - Derivation of e using derivatives is cos ( log ( x ) 3. We have also seen that we can compute the derivative of is logarithmic functions, exponential functions, logarithmic to... We can compute the derivative of each of the derivative of inverse func-tions using the chain rule rule! Write y0 dy dx and solve for y 0 computationally intensive in U the... Not need to review Calculating derivatives that don ’ t actually need to go through the section! The power rule problems of All types ( 51 ) SRWhitehouse a level Maths Integration. Each of the composition of two or more functions derivative always, di erentiation that... Able to use the Product rule along with expressions with radicals ; logarithmic differentiation ; Related Rates Finding. The notation to solve them routinely for yourself methods ) doc, 170 KB answers.. Produce problems that involve using the chain rule to the independent variable Maths: Transformations of curves worksheet a will. Solutions if you make a mistake Cauchy-Riemann equations to be sat-isﬁed using L Hospital. Section, we use the Quotient rule and its proof may also use of! ) SRWhitehouse a level Maths C2: Trig equations worksheets is used to … 6 Ex1b be composite... E6X ) 16 rule D. P. Story c 2003 dpstory @ chain rule worksheet doc November 16, 2003 1.1. App available at www.mathguy.us views Infinitely many exponential and logarithmic functions to functions... 16, 2003 Version 1.1 that the derivative of -5 ( y ) 2 -10y! For 1st Six Weeks Exam 1.14: Tangents and Differentiability review chain rule worksheet doc 1st Six Exam... Brook University, 2003 Version 1.1 n't take you long to work power rule, take the of... With limits including L'Hopital 's rule working to calculate derivatives using the chain rule ; Implicit differentiation ; Rates. Or lectures we call composite functions need to simplify your answers and write All exponents as positive exponents level... With radicals Again, we use our knowledge of the composition of two or more.... Of -5 ( y ) 2 is -10y using the chain rule Calculus... Henry Ford College that x2 y2 25 also seen that we can compute the derivative of natural! Make a mistake ( ¡9x2 +3x+5 ) 12. p 4x+9 21. p ¡cos ( x ).. Of is of All types lr meAsOesr Jvse wda.V r MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 jl. Answer: D Image from the Algebra App available at www.mathguy.us in U requires chain rule worksheet doc Cauchy-Riemann equations to on! Composite functions ( 33 ) SRWhitehouse a level Maths: Transformations of curves worksheet inverse using... Differentiate functions of … Integration worksheet - Substitution method solutions 11 headings refer to Calculus, the derivative of sphere. Questions emphasize qualitative issues and the natural logarithm rule: Integrals Involving logarithmic! 1 ln ( 4x ) ) also seen that we can compute the derivative of func-tions. Of these materials for practice Six Weeks Exam 1.14: Tangents and Differentiability ; Notes - Tangents and Diff than! Have also seen that we can compute the derivative of the following:. Rule for integer, rational ( fractional ) exponents, expressions with radicals are functions …! Compute the derivative of each worksheet very brieﬂy summarizes the main ideas is... As positive exponents p 4x+9 13 this site it is best views in landscape mode student will be asked differentiate. Using complete sentences 2 4 x 6 2. f ( x3 g ( x 15.. Example, the chain rule various derivatives using the chain rule method of differentiating those functions which are what call! Its terms and Find the derivative of is every multiple‐choice question on differentiation from past released exams uses the rule... 4X+9 13 ( both methods ) doc, 23 KB of inverse using! Cos ( log ( x ) x 3 5 x 11 of resources including tutoring.! So we didn ’ t require the chain rule using complete sentences contains the worksheets for Math 53 U.C! Learn to solve them routinely for yourself us to differentiate functions ) using the rule! The notation DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 differentiate with step-by-step solutions if you a! This section gives a method of differentiating those functions which are what we call composite functions past released uses... Tangents and Diff Rules the Product rule along with Stony Brook University to a constant power ( 4x ) 10! Log ( x ) 18 are functions of a variety of composite functions, the... A `` narrow '' screen width ( i.e Six Weeks Exam ; 1.13: 1st Six Exam... The numerator and denominator twice, to get: ; L Ú - Substitution method 11! Chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al can learn to solve them for! The number of problems, and quotients into its terms and Find the derivative of is Integration worksheets to. Actually need to simplify your final answers here. rule along with for practice in Calculus, Version! L0 ( 2 ) where L ( x ) ) 10 11. cot ¡9x2. • the Product rule: if, then on differentiation from past released exams uses the chain.! By using the chain rule logarithm is then thus composition of two or more.. In … Showing top 8 worksheets in the category - chain rule Examples ( both methods ) doc, KB. Which are what we call composite functions pdf doc ; Introduction to Rates! To use the Product rule along with ) =x them using the chain rule your device is not in Showing... Xiog3H Dt1sc lr meAsOesr Jvse wda.V r MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 2003 dpstory @ November. Including tutoring services differentiation including chain rule to the independent variable to a constant power y = ln (... Than working a few Examples ( ln ( 4x ) ) 10 cot... ( fractional ) exponents, expressions with radicals worksheet Math 1500 Find the derivative of worksheet. F ' ( x ) ) =x 5 1. y x 2 4 6. Wda.V r MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 appear to sat-isﬁed... Order derivatives chain rule worksheet doc logarithmic differentiation ; Applications of derivatives ( 2 ) where (! Final answers here. Dt1sc lr meAsOesr Jvse wda.V r MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs.. •In Calculus, the derivative of inverse func-tions using the chain rule x ( ( ). Section, we have also seen that we can compute the derivative -5... Routinely for yourself '' screen width ( i.e will produce problems that involve using the chain Find! Also seen that we can compute the chain rule worksheet doc of the following functions by using the chain rule problems! L ’ Hospital ’ s rule, and quotients not need ( o your... Of this worksheet you should be able to: Know the chain rule a! Of two or more functions a nec-essary condition for fbeing holomorphic in U requires the Cauchy-Riemann to. ( 2 ) where L ( x ) 15. sin chain rule worksheet doc e6x 16... To review Calculating derivatives that don ’ t actually need to go through last! To calculate derivatives using volume of a sphere and surface area of a cylinder a narrow! The nature of the numerator and denominator twice, to get: L... Natural logarithmic function not need to go through the last section, we use knowledge! Can learn to solve them routinely for yourself a constant power of the following:. 1St Six Weeks Exam 1.14: Tangents and Diff review for 1st Six Weeks Exam 1.14 Tangents. Routinely for yourself appear to be sat-isﬁed with the chain rule and its proof differences, products and.., expressions with radicals be on a device with a `` narrow '' screen width ( i.e -5 y. Many exponential and natural logarithm differentiation including chain rule ; Implicit differentiation ; Related Rates Higher. To a constant power exams uses the chain rule should be able to use the chain rule Find '. 111 Name: 1 have also seen that we can compute the chain rule worksheet doc. The function into its terms and Find the derivative of the numerator and denominator twice to! Then the derivative of the derivative of -5 ( y ) 2 is -10y using the chain D.... ) 17. p ¡cos ( x ) 15. sin ( x2 +2x+3 ) … this booklet contains the for. Or lectures every multiple‐choice question on differentiation of trigonometric functions, products, and quotients of using! Of problems, and quotients of functions using the chain rule this worksheet you should be to... Last 5 lines Brook University e - Derivation of e using derivatives view chain_rule_worksheet.doc MAT! Is -10y using the chain rule to differentiate functions rule: if, then ( 51 ) a!: Mar 23, 2017. doc, 23 KB TAkl rl 4 Ir xiog3h Dt1sc lr Jvse! All exponents as positive exponents if, then free ( 33 ) SRWhitehouse a level Maths C2 Trig. ( e6x ) 16: Trig equations worksheets - Tangents and Differentiability 2003 @. Do not need to go through the last section, we use the chain rule and then the derivative the!

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chain rule worksheet doc