Chain Rule

Reference > Calculus: Differentiation

Description

\[\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\]

Examples

\[\frac{d}{dx} \sin{(\ln{x})}\]

Use Chain Rule on \(\frac{d}{dx} \sin{(\ln{x})}\). Let \(u=\ln{x}\). Use Trigonometric Differentiation: the derivative of \(\sin{u}\) is \(\cos{u}\).

\[\cos{(\ln{x})}(\frac{d}{dx} \ln{x})\]

The derivative of \(\ln{x}\) is \(\frac{1}{x}\).

\[\frac{\cos{(\ln{x})}}{x}\]

Done