Primitive function/Derivative of integral from 0 to g(x) of f/Exercise

Let ${}g\colon \mathbb {R} \rightarrow \mathbb {R}$ be a differentiable function and let ${}f\colon \mathbb {R} \rightarrow \mathbb {R}$ be a continuous function. Prove that the function

${}h(x)=\int _{0}^{g(x)}f(t)dt\,$

is differentiable and determine its derivative.

Create a solution