Logarithmic Differentiation and Parametric Forms

Logarithmic Differentiation

Useful for differentiating functions where the variable appears in both the base and the exponent, such as $y = x^x$ — take the logarithm of both sides before differentiating.

Parametric Differentiation

When $x$ and $y$ are both given in terms of a third variable $t$:

$$\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$$