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Multiply both sides by f(x). f'(x) = f(x)(-11 In (x) - 11) -11x %3D -11x Substitute x for f(x) and simplify. %3D ((x) ul + L)x_(x)LL- =

Multiply both sides by f(x). f'(x) = f(x)(-11 In (x) - 11) -11x %3D -11x Substitute x for f(x) and simplify. %3D ((x) ul + L)x_(x)LL- =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For the part circled in orange. I don't understand this part or what we are doing here. 

ix Compute the derivative. Use logarithmic differentiation where appropriate. - 11x X. хр -11x %3D Let f(x) = x Then take the natural logarithm of both sides. Take the natural logarithm of each side. f(x) = -11x %3D In (f{x)) = In (x¯11×) %3D In (f(x)) = - 11x In (x) Simplify. Now take the derivative of each side. Recall that In (x): хр In (f(x)) = - 11x In (x) (()}) uj = In (x)(-11x) – 11x In (x) %3D (x),J (x) (x) u хр Apply the product rule. %3D xp = - 11 In (x) – 11xy In (x) Compute the derivative of the %3D xp = - 11 In (x) – 11 Compute the derivative of th -11x Solve for f' (x), then substitute x for f(x). (x), = - 11 In (x) - 11 (x) f'(x) = f(x)(-11 In (x) – 11) %3D Multiply both sides by f(x). - 11(x)(1 + In (x)) - 11x -11x for f(x) and simplify. %3D Substitute x Therefore, f'(x) = -11(x)11X(1 + In (x)). %3D Inf(x)D %3D 11-(X)U||- = (X)}U
Transcribed Image Text:ix Compute the derivative. Use logarithmic differentiation where appropriate. - 11x X. хр -11x %3D Let f(x) = x Then take the natural logarithm of both sides. Take the natural logarithm of each side. f(x) = -11x %3D In (f{x)) = In (x¯11×) %3D In (f(x)) = - 11x In (x) Simplify. Now take the derivative of each side. Recall that In (x): хр In (f(x)) = - 11x In (x) (()}) uj = In (x)(-11x) – 11x In (x) %3D (x),J (x) (x) u хр Apply the product rule. %3D xp = - 11 In (x) – 11xy In (x) Compute the derivative of the %3D xp = - 11 In (x) – 11 Compute the derivative of th -11x Solve for f' (x), then substitute x for f(x). (x), = - 11 In (x) - 11 (x) f'(x) = f(x)(-11 In (x) – 11) %3D Multiply both sides by f(x). - 11(x)(1 + In (x)) - 11x -11x for f(x) and simplify. %3D Substitute x Therefore, f'(x) = -11(x)11X(1 + In (x)). %3D Inf(x)D %3D 11-(X)U||- = (X)}U
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