If #f(x) =-e^(x) # and #g(x) = 3csc^2x^2 #, what is #f'(g(x)) #? Calculus Basic Differentiation Rules Chain Rule 1 Answer Alan N. Sep 3, 2017 #f'(g(x)) = -e^(3csc^2x^2)# Explanation: #f(x) = -e^x# #:.f'(x) =-d/dx e^x = -e^x# [Standard differential] #g(x) = 3csc^2x^2# Hence, #f'(g(x)) = -e^(g(x))# #:. f'(g(x)) = -e^(3csc^2x^2)# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1236 views around the world You can reuse this answer Creative Commons License