Calculus Examples

$\int_{0}^{\tan (x)} \sqrt{t} d t$

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

$\frac{d}{d x} [\tan (x)] \sqrt{\tan (x)}$

The derivative of $\tan (x)$ with respect to $x$ is $\sec^{2} (x)$ .

$\sec^{2} (x) \sqrt{\tan (x)}$