Logarithmic Differentiation

Logarithmic Differentiation

If:

$$y=f(x)$$

and taking logarithm simplifies the expression, then:

$$\ln y=\ln f(x)$$

Differentiating:

$$\frac{y'}{y}=\frac{d}{dx}[\ln f(x)]$$

Usage

- Useful for products, quotients, powers and variable exponents that are difficult to differentiate directly.