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

1 Answer

Answer:

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)#