Calculus Examples

$\int_{0}^{x^{2}} \sin (t) d t$

Take the derivative of $\int_{0}^{x^{2}} \sin (t) d t$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [x^{2}] \sin (x^{2})$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 x \sin (x^{2})$