Question

What is the derivative of \[\frac{1}{f(x)}\]?

Options

• \[-\frac{1}{[f(x)]^2}\cdot f'(x)\]

• \[[f(x)]^2\cdot f'(x)\]

• \[\frac{1}{[f(x)]^2}\cdot f'(x)\]

• \[-\frac{1}{f(x)}\cdot f'(x)\]

Answer 1

The reciprocal function has a negative derivative. The chain rule also requires multiplication by the derivative \[f'(x)\].