Question

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

Answer 1

The slope of the normal line at that point is `-1/2`

Explanation:

`dy/dx=1+1/cos^2x`

Therefore:

`(dy/dx)_(x=pi)=1+1/cos^2pi=1+(-1)^2=2`

So the slope of the tangent line is `2` and the slope of the normal line is `-1/2`