Chain rule

In differential calculus, the chain rule is a way of finding the derivative of a function. It is used where the function is within another function. This is called a composite function.

More specifically, if ${\displaystyle F(x)}$ equals the composite function of the form:

${\displaystyle F(x)=f(g(x))}$

where g is a function differentiable at x and f is a function differentiable at g(x), then the derivative of ${\displaystyle F(x)}$, written as ${\displaystyle F'(x)}$, exists, and is equal to