Question

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

Options

• \[f(x)\log a\cdot f'(x)\]

• \[\log(f(x))\cdot f'(x)\]

• \[\frac{1}{f(x)}\cdot f'(x)\]

• \[\frac{1}{f(x)\log a}\cdot f'(x)\]

Answer 1

The derivative of \[\log(f(x))\] is the reciprocal of its argument times the inner derivative. Therefore it is \[\frac{1}{f(x)}\cdot f'(x)\].