Calculus Examples

$y = \sec (u)$

Differentiate both sides of the equation.

$\frac{d}{d u} (y) = \frac{d}{d u} (\sec (u))$

The derivative of $y$ with respect to $u$ is $y'$ .

$y'$

The derivative of $\sec (u)$ with respect to $u$ is $\sec (u) \tan (u)$ .

$\sec (u) \tan (u)$

Reform the equation by setting the left side equal to the right side.

$y' = \sec (u) \tan (u)$

Replace $y'$ with $\frac{d y}{d u}$ .

$\frac{d y}{d u} = \sec (u) \tan (u)$