Question

What is the derivative of \[\log_a(f(x))\]?

Options

• \[\frac{1}{f(x)}\cdot f'(x)\]

• \[\log_a(f(x))\cdot f'(x)\]

• \[a^{f(x)}\log a\cdot f'(x)\]

• \[\frac{1}{f(x)\log a}\cdot f'(x)\]

Answer 1

A logarithm with base \[a\] has the additional factor \[\log a\] in the denominator. The chain rule requires multiplication by \[f'(x)\].