# Question #62094

Mar 2, 2016

$\frac{d}{\mathrm{dx}} \left({\sec}^{2} x\right) = 2 {\sec}^{2} x \tan x$

#### Explanation:

The derivative of $\sec x$ is $\sec x \tan x$.

$\left[1\right] \text{ } \frac{d}{\mathrm{dx}} \left({\sec}^{2} x\right)$

$\left[2\right] \text{ } = \frac{d}{\mathrm{dx}} \left[{\left(\sec x\right)}^{2}\right]$

Use power rule. We also have to use chain rule.

$\left[3\right] \text{ } = 2 {\left(\sec x\right)}^{1} \cdot \frac{d}{\mathrm{dx}} \left(\sec x\right)$

Derivative of $\sec x$ is $\sec x \tan x$.

$\left[4\right] \text{ } = 2 \left(\sec x\right) \cdot \left(\sec x \tan x\right)$

$\left[5\right] \text{ } = 2 {\sec}^{2} x \tan x$