If #f(x)= tan2 x # and #g(x) = sqrt(-4x-3 #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
Mar 11, 2018

Answer:

#-(4sec^2(2sqrt(-4x-3))) /sqrt(-4x-3)#

Explanation:

Starting with: #f(x) = tan2x# and #g(x)=sqrt(-4x-3) = (-4x-3)^(1/2)#

Let #h(x) = f(g(x)) = tan(2(sqrt(-4x-3)))#

#f'(x) = 2sec^2(2x)#
#g'(x) = (1/2)(-4)(-4x-3)^(-1/2) = -2/sqrt(-4x-3)#

Using the Chain Rule:

#h'(x) = f'(g(x))*g'(x)#

#h'(x) = 2sec^2(2sqrt(-4x-3))*-2/sqrt(-4x-3)#

#h'(x) = -(4sec^2(2sqrt(-4x-3)))/sqrt(-4x-3)#