Question

If `f(x)= sec2 x` and `g(x) = -x^2 -1`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

First, let's find our new function: `f(g(x))=sec(-2x^2-2)`

Explanation:

Now, we'll need chain rule to differentiate it.

• Chain rule: `(dy)/(dx)=(dy)/(du)(du)/(dx)`

Let's rename `u=-2x^2-2` and recall the rule to differentiate `sec` functions:

• Be `y=secu`, then `y'=u'secutanu`

`(dy)/(dx)=-4xsec(-2x^2-2)tan(-2x^2-2)`