Let be a differentiable function with for all

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

f(x)

be a differentiable function with

f(x)>0

for all

x

. Answer the following: (i) Write

\dfrac{d}{dx}\bigl[\ln(f(x))\bigr]

in terms of

f(x)

and

f'(x)

. (ii) State one reason for the form of your answer in part (i).

Related theory

Advanced Differentiation
Derivatives of standard functions via chain rule
Exponential and logarithmic functions
Continuity and Differentiability
Differentiation Rules

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