If #f(x) =-e^(-3x-7) # and #g(x) = -2sec^2x #, what is #f'(g(x)) #? Calculus Basic Differentiation Rules Chain Rule 1 Answer A. S. Adikesavan Feb 15, 2017 #=12e^(-7)e^(6sec^2x)sec^2xtanx#. Explanation: #f(g)=-e^(-3g-7)=e^(-7)e^(6sec^2x)# So, #f'(g)=(df)/(dx)# #=e^(-7)e(6sec^2x)(6sec^2x)'# #=e^(-7)e(6sec^2x)12secx(secx)'# #=12e^(-7)e^(6sec^2x)sec^2xtanx#. 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 1151 views around the world You can reuse this answer Creative Commons License