# Chain rule

The chain rule is a formula for calculating the derivative of the composition of two (or more) functions. In function notation, it can be written as $(f \circ g)'(x) = f'(g(x))\, g'(x).$

An alternative way of writing it is as follows. If $y$ is a function of $u$, and $u$ is a function of $x$, then $\frac{dy}{dx}=\frac{dy}{du}\,\frac{du}{dx}.$ For example, if $y=(x^2+3)^5$, then if we write $u=x^2+3$, we have $y=u^5$, so $\frac{dy}{dx}=5u^4\times2x=10x(x^2+3)^4.$