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

1 Answer
Jan 7, 2016

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)