Chain Rule

Reference > Calculus: Differentiation

Description
\[\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\]
Examples
\[\frac{d}{dx} \sin{(\ln{x})}\]
1
Use the Chain Rule on \(\frac{d}{dx} \sin{(\ln{x})}\). Let \(u=\ln{x}\)
The derivative of \(\sin{u}\) is \(\cos{u}\)
\[\cos{(\ln{x})}(\frac{d}{dx} \ln{x})\]

2
The derivative of \(\ln{x}\) is \(\frac{1}{x}\)
\[\frac{\cos{(\ln{x})}}{x}\]

Done

See Also