This is an application of the chain rule together with our knowledge of the derivative of ex. 12. • The chain rule • Questions 2. ��� > �� E G ���� D � T �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� U@ �� S bjbj���� .v �� �� 1 �� �� �� � b b b b B B B V �" �" �" 8 �" �# T V �I 2 J$ �. Practice is the best way to improve. (d) y= xe 2x (e) g(x) = (1 + 4x)5(3 + x x2)8 (f) y= excosx (g) F(z) = Chain Rule Practice Problems Calculus I, Math 111 Name: 1. Let (ix) Use Chain Rule. h��Vmk�8�+�ز�z�mXi�i�^�sۅ�n�&���6��fd�����6��!aDqO� ��$>�(͡���%Lz�K_����}��� �@��# Target: On completion of this worksheet you should be able to use the chain rule to differentiate functions of a function. 1 . endstream
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A student will be able to: Know the chain rule and its proof. l. Find the derivative of the following functions with respect to the independent variable. In the last section, we have learned that the derivative of is . Power Rule 1. f(x) = x x3 2. f(x) = 4 x2 x2 4 3. h(x) = 3 p x 4. f(x) = x2 e2 5. g(x) = pp x 6. f(x) = x2 1 x 7. f(x) = 7x+ 3x2 5 p x Chain Rule Find the rst derivative of the following functions: 8. f(x) = (x2 1)10 9. f(x) = p 1 + p 1 + 2x 10. g(x) = (3x2 + 3x 6) 8 11. f(x) = 4 p 9 x Product and Quotient Rule Find the rst derivative of the following functions: 12. f(x) = (x+ 1)(x2 3) (Try this one in two di erent ways.) ]a?�P�@렆�h$x{D"u�/cľIN�Ȼ���d�B,ke
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2O��V�BQTHG�dO�qbf�܊�D&�@�N; ��#xio The questions emphasize qualitative issues and the problems are more computationally intensive. 0) = f0(g(z0))g(z0) (chain rule): (2.8) Complex differentiability is closely related to the Cauchy-Riemann equations [Lang, 1993]. The additional problems are more challenging and sometimes deal … 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. 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), … You appear to be on a device with a "narrow" screen width (i.e. These Calculus Worksheets will produce problems that involve using the chain rule to differentiate functions. Next Section . Title: Calculus: Differentiation using the chain rule. INTRODUCTION. d dx (e3x2)= deu dx where u =3x2 = deu du × du dx by the chain rule = eu × du dx = e3x2 × d dx (3x2) =6xe3x2. Chain Rule; Implicit Differentiation; Related Rates; Higher Order Derivatives; Logarithmic Differentiation; Applications of Derivatives. HW #10 - Chain Rule; HW #10 - Answer Key; 1.11: Inverse Trig Derivatives. (Y rewviìe'. … (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. ... Limit Practice-Additional practice with limits including L'Hopital's Rule. Solution: We use the Quotient Rule and the natural logarithm rule: Integrals Involving Natural Logarithmic Function. 6 Ex1b. … Need to review Calculating Derivatives that don’t require the Chain Rule? Your instructor might use some of these in class. ©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. e use the chain rule here where y is the “inner” function. By using the Chain Rule an then the Power Rule, we get = = nu;1 = n*g(x)+;1g’(x) VCE Maths Methods - Chain, Product & Quotient Rules The product rule 4 • The product rule is used to … -5x)4 r (k) k) 3 Mobile Notice. The Power Rule for integer, rational (fractional) exponents, expressions with radicals. 3 y' = 4 cos2(3.r)cos( 4x) + - 6 sin( 4x) cos( 3x)( sin 3x) 2. Home / Calculus I / Derivatives / Chain Rule. ¡cos(ln(4x)) 5. Simplify your answers and write all exponents as positive exponents! g Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Differentiation - Quotient Rule Date_____ Period____ c r TAkl rl 4 Ir xiog3h Dt1sc lr meAsOesr Jvse wda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8. 03 - Chain Rule Top cdn.kutasoftware.com ©F f2h0 21D34 0K muFt HaQ DSBo cf DtEw XaErXe2 BLRLYC7. Showing top 8 worksheets in the category - Chain Product And Quotient Rules. The Organic Chemistry Tutor 1,090,721 views The antiderivative is . endstream
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The method is called the chain rule. A worksheet on differentiation of trigonometric functions, logarithmic functions, exponential functions, products and quotients of functions using the chain rule. 2. (sin(x))10 20. doc, 90 KB. For problems 1 – 6 use the Product Rule or the Quotient Rule to find the derivative of the given function. The Chain Rule for composite functions. 2¡9x2+3x+5 10. To differentiate this we write u = (x3 + 2), so that y = u2 Also applies to subtraction in the same way. (sin(x))100 4. 1 ln(4x) 17. p ¡cos(x) 18. You may select the number of problems, and the notation. Answer: D Image from the Algebra App available at www.mathguy.us.
Apply the chain rule to the calculation of the derivative of a variety of composite functions. Example 5: Find the derivative of . 1. Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the chain rule. One. Students will be able to. 10. 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. 6 !`�$�?�OY��rN
"��W�y�w]�� 8����C�F����;" ���A��+H��O�i�������Gs�9G��>vA_m���� u#� (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. (a) F(x) = 4 p 1 + 2x+ x3 (b) g(t) = 1 (t4 + 1)3 (c) y= cos(a3 + x3) where ais a constant. Show Mobile Notice Show All Notes Hide All Notes. Lecture 10: Worksheet The chain rule The rule(f(g(x))0= f0(g(x))g0(x) is called the chain rule. Page | 5 Part II: Multiple Choice: Calculators Are Allowed Use implicit differentiation: : Û E Û ; L : Ú ß â ; Û E Û L Ù L F L F Þ ? Tools for Success-A list of resources including tutoring services. Integration Worksheet - Substitution Method Solutions 11. Ú Û L Þ Ú Û So, the slope of the tangent line, L Þ Ú Û Ú Û E Ú Ý Ý L Þ … (b) Suppose f and gare di erentiable functions so that f(2) = 3, f0(2) = 1, g(2) = 1 4, and g0(2) = 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. Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by 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. Derivatives. doc, 170 KB. 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). The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al. So we didn’t actually need to go through the last 5 lines. 5 1. y x 2 4 x 6 2. f ( x) x 3 5 x 11. Simplify your answers and write all exponents as positive exponents! No calculator unless otherwise stated. 1 Find the derivative of p 1 + x2 using the chain rule Bring the exponent to the front … Prev. Rates of Change; Critical Points; Minimum and Maximum Values; Finding Absolute Extrema; The Shape of a Graph, Part I; The Shape of a Graph, Part II; The Mean Value Theorem; Optimization; More Optimization Problems; L'Hospital's Rule and Indeterminate Forms; … Find each of the following: i. h0(2) where h(x) = p [f(x)]2 + 7. ii. How to use the Chain Rule. We want to derive a rule for the derivative of a composite function of the form in terms of the derivatives of f … This is a brief tutorial on how to enter your answers View US version. For example, the derivative of sin(log(x)) is cos(log(x))=x. 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 … Berkeley’s multivariable calculus course. Find the derivatives of the given functions. 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. … �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�!�� Name_____ Use the power, product, quotient, and chain rules to find the derivative of the following functions. Date_ Period_ (1) f (x) = sin(3x) (2) f (x) = cos(7x) (3) f (x) = (4x2 + Title: Calculus: Differentiation using the chain rule. ©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 Name_____ Use the power, product, quotient, and chain rules to find the derivative of the following functions. The introduction of each worksheet very brieﬂy summarizes the main ideas but is not intended as a substitute for the textbook or lectures. We have also seen that we can compute the derivative of inverse func-tions using the chain rule. The student will be given composite functions and will be asked to differentiate them using the chain rule. Solution Again, we use our knowledge of the derivative of ex together with the chain rule. Section. Z ˇ 0 cos(x) p sin(x) dx (a)Let u= sin(x) (b)Then du= cos(x) dx (c)If x= 0, then u= sin(0) = 0. Show all files. 1. log13 (8x3 +8) 2. pdf doc ; Chain Rule - Practice using this rule. Solution: Here we use the Product Rule along with . 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. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx Chain Rule: Problems and Solutions. •Prove the chain rule •Learn how to use it •Do example problems . Power Rule; Exponentials and Logs; Trigonometric Functions; Sum Rule; Product Rule; Quotient Rule; Chain Rule; All Types ; Derivative Worksheets. Showing top 8 worksheets in the category - Chain Rule. 6 2. (a) Carefully state the chain rule using complete sentences. pdf doc ; Introduction to Related Rates - Finding various derivatives using volume of a sphere and surface area of a cylinder. Differentiation Using the Chain Rule. Chain Rule Examples (both methods) doc, 170 KB. 22 0 obj
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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 … Notes - Tangents and Differentiability; Notes - Tangents and Diff. • The chain rule • Questions 2. Find the derivative of the following functions with respect to the independent variable. The following is a list of worksheets and other materials related to Math 122B and 125 at the UA. Separate the function into its terms and find the derivative of each term. 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. 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. Chain Rule Practice Problems Calculus I, Math 111 Name: 1. Y = x 2 +4x+6) 3. It shouldn't take you long to work power rule problems of all types. Title: Practice Exercise Sheet 1 Author: cwhelan Last modified by: TCD User Created Date: 10/3/2005 3:49:00 PM About this resource. Nearly every multiple‐choice question on differentiation from past released exams uses the Chain Rule. Let . Section 3-4 : Product and Quotient Rule. l0(2) where l(x) = f(x3 g(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. This booklet contains the worksheets for Math 53, U.C. 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 Students will be able to. Using L’Hospital’s Rule, take the derivatives of the numerator and denominator twice, to get : ; L Ú. If the argument of the natural logarithm is then thus . 9. 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 chain rule allows us to differentiate composite functions. Apply when x is raised to a constant power. Example Find d dx (e x3+2). 8. Nearly every multiple‐choice question on differentiation from past released exams uses the Chain Rule. How to use the Chain Rule. Show Mobile Notice Show All Notes Hide All Notes. Definition •In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. Let and (viii) Use Chain Rule. Here we use the Chain Rule: Example 4: Find the derivative of . This section gives a method of differentiating those functions which are what we call composite functions. (f) y = sin x L ox did 3 3x (d) y = csc (g) Y = x tan— Page I … Notes - Section 2.6 part 1; 2018 AB #5; Notes - Section 2.6 part 1 (filled) HW #11 - Inverse Trig Derivatives; HW #11 - Answer Key; 1.12: 1st Six Weeks Review. Apply the chain rule to the calculation of the derivative of a variety of composite functions. 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 No calculator unless othenvise stated. (filled) … 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. Prev. Implicit differentiation worksheet pdf. Notes Practice Problems Assignment Problems. In terms of xand y, the function f(z) can be … Calculus I Worksheet Chain Rule Find the derivative of each of the following functions. 3 p 4x+9 21. p ¡cos(x) 22. FREE (33) SRWhitehouse A level Maths C2: Trig equations worksheets. A student will be able to: Know the chain rule and its proof. ¡cos(4x+9) 3. You appear to be on a device with a "narrow" screen width (i.e. Then add up the derivatives. The Chain Rule D. P. Story c 2003 dpstory@uakron.edu November 16, 2003 Version 1.1. doc, 90 KB. pdf doc ; Base e - Derivation of e using derivatives. %%EOF
You may also use any of these materials for practice. Composite functions are functions of … Info. Derivatives of sum, differences, products, and quotients. �^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�>�� View chain_rule_worksheet.doc from MAT MISC at Stony Brook University. Learning Objectives . (You do not need to simplify your final answers here.) ©v G2r0Q1 H3O pK nu atEa 9 ZSVoGfutQw5a 5r Xe V RL xLpCW.8 Y hAnlQl0 vr liJgWh3t qsO drRe8s 5e Yrjv seTdr. 2���J��� w�1
(You do not need (o simplify your final answers here.) (¡9x2 +3x+5)100 6. pp x 7. tan(ln(4x)) 8. cos(ln(x)) 9. Quick Refresher. Use the chain rule in Lagrange (Prime) Notation. Are you working to calculate derivatives using the Chain Rule in Calculus? Published by Wiley. epwrp)e is Calculus Worksheet Chain Rule Practice #1 Find the derivative of each of the following functions. Find the derivative of the given function. The Chain Rule for composite functions. 1. x100 ⇒ 2. x−100 ⇒ 3. View Chain Rule Examples.doc from MATH 225 at Henry Ford College. H���=O1ཿ�FX�$�8� endstream
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Let . If your device is not in … Differentiation Using the Chain Rule. Exercises 3.1. 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 … The Power Rule . Worksheet Derivatives Implicit Differentiation Chain Rule Calculus Printable . 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. A find dy dx by implicit di erentiation given that x2 y2 25. h�bbd``b`� $�� ��SL "Dx��� ̛AD=H,D� ���$H\�a`bdX Worksheet 2.6—The Chain Rule Short Answer Show all work, including rewriting the original problem in a more useful way. SRWhitehouse A level Maths: Transformations of curves worksheet. 13. g(x) = 3x2 + 5x p x … Differentiation Using the Chain Rule. Z (x+1)sin(x2 +2x+3) … 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, … 1. log13 (8x3 +8) 2. y = x3 + 2 is a function of x y = (x3 + 2)2 is a function (the square) of the function (x3 + 2) of x. Since the slope is the derivative of the function evaluated at the given … Section. ˺. (You do not need (o simplify your final answers here.) 2 Prerequisite: Tutorial on the AcroTEX System of Online Assessment You must enter your answer in the response boxes using a certain “natural” syntax. Created: Dec 4, 2011. 2 write y0 dy dx and solve for y 0. Infinitely many exponential and logarithmic functions to differentiate with step-by-step solutions if you make a mistake. Chain Rule Worksheets. Derivatives - Power, Product, Quotient and Chain Rule - Functions & Radicals - Calculus Review - Duration: 1:01:58. Find the derivative of the given function. … A nec-essary condition for fbeing holomorphic in U requires the Cauchy-Riemann equations to be sat-isﬁed. ... Other resources by this author. Due to the nature of the mathematics on this site it is best views in landscape mode. Find the derivative of y = 8 4x2 +7x+28 4 Answer: y0 = 32(8x + 7) 4x2 + 7x + 28 3 a = 8, n = 4 u = 4x2 +7x+28 ⇒ du dx = 8x+7 ⇒ y0 = … The Power Rule for integer, rational (fractional) exponents, expressions with radicals. doc, 170 KB. H����N1�����I��C�BQ�Ω7�WE[� HW #12 - Review for 1st Six Weeks Exam ; 1.13: 1st Six Weeks Exam 1.14: Tangents and Differentiability. 39 0 obj
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Problems may contain constants a, b, and c. 1) f (x) = 3x5 f' (x) = 15x4 2) f (x Chain Rule Examples Name_ Find f '(x) using the chain rule. There is nothing better than working a few examples. Report a problem. (d) y= xe 2x (e) g(x) = (1 + 4x)5(3 + x x2)8 (f) y= excosx (g) F(z) = doc, 90 KB. Let’s solve some common problems step-by-step so you can learn to solve them routinely for yourself. 3.3 The Chain Rule. Learning Objectives . 3.3 The Chain Rule. 0
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FREE (51) SRWhitehouse A level Maths: Integration worksheets. Differentiate the following functions: Use rule y = ln x ( (vii) Use the product rule: If , then . 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. l. Find the derivative of the following functions with respect to the independent variable. 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 … 03 - Chain Rule Live cdn.kutasoftware.com ©F f2h0 21D34 0K muFt HaQ DSBo cf DtEw XaErXe2 BLRLYC7. Report a problem. c r TAkl rl 4 Ir xiog3h Dt1sc lr meAsOesr Jvse wda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve 6 XCta jl Qc3uwlfuxs 8. Derivatives of sum, differences, products, and quotients. 1 x5 ⇒ 4. xπ ⇒ 5. x3/4 ⇒ 6. x−9/7 ⇒ 60 Chapter 3 Rules for Finding Derivatives 3.2 rity Linea of the tive a Deriv An operation is linear if it behaves “nicely” with respect to multiplication by a constant and … l&�(�{�ę�f|hS3�fL
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