# Question #bb2ac

Feb 7, 2018

$\sin x + x \cos x + {\sec}^{2} x$

#### Explanation:

The first term of the derivative can be simplified to $x \sin x$. This is why you spend all those agonizing hours doing trig identities!

$x \tan \frac{x}{\sec} x = \frac{x \sin \frac{x}{\cos} x}{\frac{1}{\cos} x} = x \sin \frac{x}{\cos} x \cdot \cos x = x \sin x$

So now your function looks like this:

$x \sin x + \tan x$

Take the derivative of each term separately, using the product rule for the first term.

$\left(\sin x + x \cos x\right) + {\sec}^{2} x$