What is $\frac{d}{dx}\int_0^{x^2} \cos t\,dt$?

Explanation

1. 01

   The integral is $\sin(x^2)$, since $\int_0^u \cos t\,dt = \sin u$.

2. 02

   By the chain rule its derivative is $\cos(x^2) \cdot 2x$.