# What is the first derivative of x+ tanx and how do you find the slope of the normal to the curve where x=pi?

Aug 21, 2015

The slope of the normal line at that point is $- \frac{1}{2}$

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 + \frac{1}{\cos} ^ 2 x$

Therefore:

${\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{x = \pi} = 1 + \frac{1}{\cos} ^ 2 \pi = 1 + {\left(- 1\right)}^{2} = 2$

So the slope of the tangent line is $2$ and the slope of the normal line is $- \frac{1}{2}$