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

1 Answer
Jul 18, 2017

Answer:

#f'(g(x)) = (xe^(sqrt(1-x^2)))/sqrt(1-x^2)#

Explanation:

#f(x) =-e^x# and #g(x) = sqrt(1-x^2)#

#:. f(g(x)) = -e^(sqrt(1-x^2)#

Applying the chain rule:

#f'(g(x)) = -e^(sqrt(1-x^2))* d/dx (sqrt(1-x^2))#

Applying the chain rule agsin:

#f'(g(x)) = -e^(sqrt(1-x^2))* 1/2 (1-x^2)^(-1/2) * d/dx(1-x^2)#

Applying the chain rule agsin:

#f'(g(x)) = -e^(sqrt(1-x^2))* 1/2 (1-x^2)^(-1/2)* (-2x)#

#= (xe^(sqrt(1-x^2)))/sqrt(1-x^2)#