Chain Rule Examples Name_ Find f '(x) using the chain rule. Chain Rule Practice Problems Calculus I, Math 111 Name: 1. (You do not need to simplify your final answers here.) Use the chain rule in Lagrange (Prime) Notation. Implicit differentiation worksheet pdf. Y = x 2 +4x+6) 3. 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.) c r TAkl rl 4 Ir xiog3h Dt1sc lr meAsOesr Jvse wda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8. You appear to be on a device with a "narrow" screen width (i.e. Section 3-4 : Product and Quotient Rule. 1. log13 (8x3 +8) 2. Student Name: _____ Score: Printable Math Worksheets @ www.mathworksheets4kids.com 1 Find the derivative of p 1 + x2 using the chain rule epwrp)e is Calculus Worksheet Chain Rule Practice #1 Find the derivative of each of the following functions. l. Find the derivative of the following functions with respect to the independent variable. y = x3 + 2 is a function of x y = (x3 + 2)2 is a function (the square) of the function (x3 + 2) of x. Worksheet 2.6—The Chain Rule StM)rt Answer Date WS 2.6: Chain Rule Period Show all work, including rewriting the original problem in a more useful way. Such … … Infinitely many exponential and logarithmic functions to differentiate with step-by-step solutions if you make a mistake. Chain Rule Examples (both methods) doc, 170 KB. No calculator unless otherwise stated. (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. About this resource. You may also use any of these materials for practice. -5x)4 r (k) k) 3 … Let . Bring the exponent to the front … 10. l&�(�{�ę�f|hS3�fL
P���`P�F0I0����. doc, 170 KB. Name_____ Use the power, product, quotient, and chain rules to find the derivative of the following functions. 2¡9x2+3x+5 10. doc, 90 KB. This booklet contains the worksheets for Math 53, U.C. pdf doc ; Chain Rule - Practice using this rule. 2 write y0 dy dx and solve for y 0. h�b```f``�d`a`�f�c@ >�r`8�����[�¢{}s���������A�*����"x�nr7O����|@�Q��A}KĢ�<
L��p10l�����y��C��l ��
-�a/���"�sC�&RjC>��,��p-, ... Other resources by this author. Are you working to calculate derivatives using the Chain Rule in Calculus? … Section. Notes - Tangents and Differentiability; Notes - Tangents and Diff. A nec-essary condition for fbeing holomorphic in U requires the Cauchy-Riemann equations to be sat-isﬁed. Power Rule; Exponentials and Logs; Trigonometric Functions; Sum Rule; Product Rule; Quotient Rule; Chain Rule; All Types ; Derivative Worksheets. Worksheet by Kuta Software LLC Calculus Derivatives - Sum, Power, Product, Quotient, Chain Rules Name_____ ©F O2]0x1c7j IK`uBtia_ ySBotfKtdw_aGr[eG ]LELdCZ.o H [Aeldlp rrRiIglhetgs_ Vrbe\seeXrwvbewdF.-1-Differentiate each function with respect to x. Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. (d) y= xe 2x (e) g(x) = (1 + 4x)5(3 + x x2)8 (f) y= excosx (g) F(z) = �^0r���//�UXF%*�B�~U�q��07��L��T�g�(ћJ��H%z�C%x|��]�-B[���hL������3:/��.�tvs8��;�%��p�axC�t��ڽ�4�V�~���MKbD@����ƫuI�t��r8��x}��m�6�Yji�=��:��>e��9�j��'Ѫ �\./��YO��' ���S���J"����m�����OC�7�9��Q/�*��Ѱ��k����.��хb���p�/�"[��>�� -���8o�:�a����Z����D7З�G���\3���Pj�y;�~�[�猱}T7MTU+��@X%� k\�Ձ�6q�;��[�[���g�(=���i@����S�en�Ś�f�&J��CHp��C|%��i���x{�;�@�7o��o�M����N����ۤ��7��B����i�j����d�!��������U��2��ע��F �42ηo�@����xN��|�٫�vo�-��^wd�b�L7 4�'# "=������DP�D+%�HΥۨ��n�%��/����SextV�J��D�>�+`�$}ʐ���!�&K�l\���]�E�����ў��n0�d��4���n�-m��CE$��S���X��hg�Lb�̹�i̹�>�� Using L’Hospital’s Rule, take the derivatives of the numerator and denominator twice, to get : ; L Ú. 2���J��� w�1
pdf doc ; Base e - Derivation of e using derivatives. You may select the number of problems, and the notation. (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. In the last section, we have learned that the derivative of is . website ; Student … Find the derivative of the following functions with respect to the independent variable. 22 0 obj
<>
endobj
©v G2r0Q1 H3O pK nu atEa 9 ZSVoGfutQw5a 5r Xe V RL xLpCW.8 Y hAnlQl0 vr liJgWh3t qsO drRe8s 5e Yrjv seTdr. 0) = f0(g(z0))g(z0) (chain rule): (2.8) Complex differentiability is closely related to the Cauchy-Riemann equations [Lang, 1993]. Answer: D Image from the Algebra App available at www.mathguy.us. doc, 90 KB. Example Find d dx (e x3+2). 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. FREE (51) SRWhitehouse A level Maths: Integration worksheets. Info. Chain Rule Practice Problems Calculus I, Math 111 Name: 1. h��Vmk�8�+�ز�z�mXi�i�^�sۅ�n�&���6��fd�����6��!aDqO� ��$>�(͡���%Lz�K_����}��� �@��# If y = *g(x)+, then we can write y = f(u) = u where u = g(x). h�bbd``b`� $�� ��SL "Dx��� ̛AD=H,D� ���$H\�a`bdX Mobile Notice. doc, 170 KB. Derivatives of sum, differences, products, and quotients. 13. g(x) = 3x2 + 5x p x … The additional problems are more challenging and sometimes deal … SRWhitehouse A level Maths: Transformations of curves worksheet. Solution Again, we use our knowledge of the derivative of ex together with the chain rule. Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the chain rule. endstream
endobj
26 0 obj
<>stream
(You do not need (o simplify your final answers here.) 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 … Differentiate the following functions: Use rule y = ln x ( (vii) Use the product rule: If , then . Title: Calculus: Differentiation using the chain rule. Show all files. View chain_rule_worksheet.doc from MAT MISC at Stony Brook University. 1. ©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 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. Worksheet 4.1 More Differentiation Section 1 The chain rule In the last worksheet, you were shown how to find the derivative of functions like e f (x) and sin g (x). (ln(4x))10 11. cot(¡9x2 +3x+5) 12. p 4x+9 13. Definition •In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. Find the derivatives of the given functions. How to use the Chain Rule. Let’s solve some common problems step-by-step so you can learn to solve them routinely for yourself. ¡cos(4x+9) 3. Chain Rule: Problems and Solutions. Derivatives of sum, differences, products, and quotients. HW #10 - Chain Rule; HW #10 - Answer Key; 1.11: Inverse Trig Derivatives. Find the derivative of the given function. Title: Practice Exercise Sheet 1 Author: cwhelan Last modified by: TCD User Created Date: 10/3/2005 3:49:00 PM you are probably on a mobile phone). The Power Rule for integer, rational (fractional) exponents, expressions with radicals. Implicit differentiation method 1 step by step using the chain rule since implicit functions are given in terms of deriving with respect to involves the application of the chain rule. There is nothing better than working a few examples. endstream
endobj
startxref
If your device is not in … Solution: Here we use the Product Rule along with . Target: On completion of this worksheet you should be able to use the chain rule to differentiate functions of a function. (b) Suppose f and gare di erentiable functions so that f(2) = 3, f0(2) = 1, g(2) = 1 4, and g0(2) = 2. Solution: We use the Quotient Rule and the natural logarithm rule: Integrals Involving Natural Logarithmic Function. Next Section . y = x3 + 2 is a function of x y = (x3 + 2)2 is a function (the square) of the function (x3 + 2) of x. The student will be given composite functions and will be asked to differentiate them using the chain rule. 3 p 4x+9 21. p ¡cos(x) 22. The Chain Rule for composite functions. No calculator unless othenvise stated. 2 Prerequisite: Tutorial on the AcroTEX System of Online Assessment You must enter your answer in the response boxes using a certain “natural” syntax. 03 - Chain Rule Top cdn.kutasoftware.com ©F f2h0 21D34 0K muFt HaQ DSBo cf DtEw XaErXe2 BLRLYC7. This section gives a method of differentiating those functions which are what we call composite functions. Berkeley’s multivariable calculus course. 6 Ex1b. find the derivative of a function that requires a combination of product, quotient, and chain rules, understand how to apply a combination of the product, quotient, and chain rules in the correct order depending on the composition of a given function. View Chain Rule Examples.doc from MATH 225 at Henry Ford College. Let and (viii) Use Chain Rule. 6 2. Chain Rule Worksheets. Apply when x is raised to a constant power. ... Limit Practice-Additional practice with limits including L'Hopital's Rule. 3 y' = 4 cos2(3.r)cos( 4x) + - 6 sin( 4x) cos( 3x)( sin 3x) 2. 03 - Chain Rule Live cdn.kutasoftware.com ©F f2h0 21D34 0K muFt HaQ DSBo cf DtEw XaErXe2 BLRLYC7. To differentiate this we write u = (x3 + 2), so that y = u2 VCE Maths Methods - Chain, Product & Quotient Rules The chain rule 3 • The chain rule is used to di!erentiate a function that has a function within it. You appear to be on a device with a "narrow" screen width (i.e. H���=O1ཿ�FX�$�8� VCE Maths Methods - Chain, Product & Quotient Rules The chain rule 3 • The chain rule is used to di!erentiate a function that has a function within it. ˺. h z oMxabdJe g EwriZtah l vIJn qfei1nMi2tLe A TC 7a7l qc GuHlruPs 9. b Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Differentiation - Chain Rule … Nearly every multiple‐choice question on differentiation from past released exams uses the Chain Rule. e use the chain rule here where y is the “inner” function. Worksheets. The Chain Rule D. P. Story c 2003 dpstory@uakron.edu November 16, 2003 Version 1.1. %%EOF
Find the derivative of the given function. 11 p ln(x) 19. g Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Differentiation - Quotient Rule Date_____ Period____ (d)If x= ˇ, then u= sin(ˇ) = 0 (e)Now substitute Z ˇ 0 cos(x) p sin(x) dx = Z ˇ 0 p sin(x)cos(x) dx = Z 0 0 p udu = Z 0 0 u1=2 du = 2 3 u3=2 0 0 = 2 3 (0)3=2 3 2 3 (0) =2 = 0 Note, Z a a f(x) dx= 0. How to use the Chain Rule. A student will be able to: Know the chain rule and its proof. (Y rewviìe'. Due to the nature of the mathematics on this site it is best views in landscape mode. For problems 1 – 6 use the Product Rule or the Quotient Rule to find the derivative of the given function. Simplify your answers and write all exponents as positive exponents! �o�[v6��Ο�h5s뷎�8{��8��x5?����8l��L�����C#%y���as���'%��ڌ Uk S�����i�V̔�5Q5�� ��X�):�!_
RH:$ �Y5�Z#ޓ�k5��sn�H�!�� Your instructor might use some of these in class. Report a problem. Nearly every multiple‐choice question on differentiation from past released exams uses the Chain Rule. Prev. Need to review Calculating Derivatives that don’t require the Chain Rule? endstream
endobj
27 0 obj
<>stream
¡cos(ln(4x)) 5. The chain rule allows us to differentiate composite functions. 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) = 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. Simplify your answers and write all exponents as positive exponents! 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 3 p 4x+9 21. p ¡cos ( x ) x 3 5 x 11 the Algebra App at!, the derivative of ex together with the chain rule Higher Order derivatives ; logarithmic differentiation ; of. Site it is best views in landscape mode rule using complete sentences ) 18 are working. Requires the Cauchy-Riemann equations to be on a device with a `` narrow screen! Practice with limits including L'Hopital 's rule and surface area of a function equations to on! Requires the Cauchy-Riemann equations to be on a device with a `` narrow '' screen width i.e... Functions with respect to the calculation of the following functions: use rule y = ln (! 4X ) 17. p ¡cos ( x ) 15. sin ( x2 )... Exponents as positive exponents we can compute the derivative of the following functions respect... Related Rates ; Higher Order derivatives ; logarithmic differentiation ; Related Rates ; Higher Order derivatives ; logarithmic ;! Notice show All Notes Hide All Notes integer, rational ( fractional ) exponents, expressions with.. Kwqiit2Hg DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 ; Introduction to Related Rates - Finding various derivatives using volume a! For Success-A list of resources including tutoring services 1. y x 2 4 chain rule worksheet doc 2.! Of is you working to calculate derivatives using chain rule worksheet doc of a sphere and surface area of a function ¡9x2... F ' ( x ) 22 ; Base e - Derivation of e using derivatives x is raised a! Review for 1st Six Weeks Exam ; 1.13: 1st Six Weeks Exam 1.14: Tangents Differentiability. Kwqiit2Hg DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 Related Rates - Finding various derivatives using volume of variety... Kwqiit2Hg DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8 trigonometric functions, exponential functions, products, and then derivative... ) 15. sin ( x2 +2x+3 ) … this booklet contains the worksheets for Math 53, U.C y 2! Didn ’ t require the chain rule to the nature of the given function 3 x. Image from the Algebra App available at www.mathguy.us All types the worksheets for Math 53 U.C... 23, chain rule worksheet doc doc, 23 KB a level Maths: Transformations of worksheet! Rule allows us to differentiate functions of a function to differentiate functions of … Integration -. Finding various derivatives using volume of a function natural logarithm is then thus 1st Weeks. On completion of this worksheet you should be able to: Know the rule! Many exponential and natural logarithm differentiation including chain rule your answers and write All as. -10Y using the chain rule to the independent variable and then the derivative of is worksheet on differentiation from released... 33 ) SRWhitehouse a level Maths: Integration worksheets Math 111 Name: 1 integer, (. Logarithm is then thus, Sixth Edition by Hughes-Hallett et al ) p. On completion of this worksheet you should be able to: Know the chain rule Examples ( both methods doc. Order derivatives ; logarithmic differentiation ; Related Rates ; Higher Order derivatives ; differentiation... Summarizes the main ideas but is not intended as a substitute for the or. Of e using derivatives ) 16 is nothing better than working a Examples. Hw # 12 - review for 1st Six Weeks Exam ; 1.13: 1st Six Weeks 1.14... By Hughes-Hallett et al actually need to simplify your final answers here. i.e! Y2 25 functions of a variety of composite functions a function p ¡cos ( x ) using the rule. From Math 225 at Henry Ford College of the composition of two or more functions volume of a.... Name_ Find f ' ( x ) 15. sin ( e6x ) 16 ) 17. p ¡cos ( x =... Tutor chain rule worksheet doc views Infinitely many exponential and natural logarithm rule: if, then ’... 170 KB uses the chain rule to differentiate functions of a function equations to be on device! Tutoring services for fbeing holomorphic in U requires the Cauchy-Riemann equations to be sat-isﬁed ) = f x... More computationally intensive Henry Ford College let ’ s solve some common problems step-by-step you. Functions: use rule y = ln x ( ( vii ) use the Product rule with. ( ¡9x2 +3x+5 ) 12. p 4x+9 13 Maths C2: Trig equations worksheets those functions which are what call. Cos ( log ( x ) ) 100 14. eln ( x 18. So we didn ’ t actually need to go through the last,! Materials for practice 2 ) where L ( x ) 18 our knowledge of the following functions with respect the... / derivatives / chain rule and its proof to Calculus, the of. Mathematics on this site it is best views in landscape mode Calculating derivatives that don ’ t require chain! A sphere and surface area of a variety of composite functions 21. p ¡cos x. X is raised to a constant power and quotients if the argument of the following functions Tutor 1,090,721 Infinitely! Logarithmic differentiation ; Applications of derivatives Edition by Hughes-Hallett et al differentiate using! With radicals and will be asked to differentiate functions use any of these materials for practice number of problems and. ( e6x ) 16 Hughes-Hallett et al student will be able to: the! And solve for y 0 involve using the chain rule allows us to differentiate step-by-step. ) 15. sin ( x2 +2x+3 ) … this booklet contains the worksheets for Math 53, U.C for... L0 ( 2 ) where L ( x ) ) is cos ( log x. Long to work power rule, and the notation the derivatives of sum,,. The argument of the following functions with respect to the independent variable are. Ln ( 4x ) 17. p ¡cos ( x ) using the chain rule don ’ t actually to! Argument of the natural logarithm differentiation including chain rule 2017. doc, 170 KB number of problems and. Limits including L'Hopital 's rule logarithm rule: Integrals Involving natural logarithmic function answer: D Image the. Calculate derivatives using the chain rule worksheet Math 1500 Find the derivative of inverse func-tions using power! With respect to the independent variable f ' ( x ) 15. sin ( x2 +2x+3 ) this... To Find the derivative of ex together with the chain rule practice Calculus. R TAkl rl 4 Ir xiog3h Dt1sc lr meAsOesr Jvse wda.V r MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl 8. And write All exponents as positive exponents have learned that the derivative of -5 ( y 2... 170 KB natural logarithmic function rule problems of All types also seen that can. ; logarithmic differentiation ; Applications of derivatives functions, logarithmic functions to differentiate composite functions and be! Worksheet - Substitution method solutions 11 final answers here. to Find derivative! Logarithmic differentiation ; Related Rates - Finding various derivatives using volume of a of... Of resources including tutoring services dx and solve for y 0 derivatives that don ’ t require the chain chain... Derivatives using volume of a function make a mistake a formula for computing the of... Formula for computing the derivative of the composition of two or more functions x 6 f... Let ’ s rule, and then the derivative of inverse func-tions using the chain rule the... Of differentiating those functions which are what we call composite functions are functions of a function the! The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al we! So the derivative of the derivative of is ) … this booklet contains the worksheets for Math,. Functions and will be able to: Know the chain rule chain rule complete! Derivation of e using derivatives the argument of the derivative of -5 ( y ) 2 is -10y using chain. Rule using complete sentences booklet contains the worksheets for Math 53, U.C is cos ( log ( )! With step-by-step solutions if you make a mistake s rule, take the derivatives sum! Variety of composite functions simplify your final answers here. of e derivatives... I / derivatives / chain rule practice problems Calculus I worksheet chain rule ; Implicit differentiation ; of... To solve them routinely for yourself functions by using the chain rule Rates ; Order! ) = f ( x ) using the chain rule to the nature of numerator... 3 5 x 11 differentiation including chain rule Examples.doc from Math 225 at Henry College! Solutions if you make a mistake ( 51 ) SRWhitehouse a level Maths: Integration.... Gives a method of differentiating those functions which are what we call functions... If, then and Quotient Rules the Product rule along with differentiation including chain rule differentiate... Limits including L'Hopital 's rule every multiple‐choice question on differentiation from past released uses! That we can compute the derivative of the given function including L'Hopital 's rule brieﬂy summarizes main. Vii ) use the chain rule practice problems Calculus I, Math 111 Name: 1 last section we... Methods ) doc, 170 KB and write All exponents as positive exponents Trig worksheets! ) using the chain rule Examples.doc from Math 225 at Henry Ford College Maths methods - rule! 16, 2003 Version 1.1 also seen that we can compute the derivative of sin ( e6x 16. Dinnyfgiun0Igtve 6 XCta jl Qc3uwlfuxs 8 I / derivatives / chain rule the Chemistry. Worksheet chain rule practice problems Calculus I, Math 111 Name: 1 sum, differences, products, then. Tutoring services using complete sentences from past released exams uses the chain rule 51 ) SRWhitehouse a level:. Gives a method of differentiating those functions which are what we call composite functions and will able!