How do you differentiate #f(x)=sec^2(e^(x) ) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Trevor Ryan. Aug 30, 2016 #d/dxsec^2(e^x)=2e^xsec^2(e^x)tan(e^x)# Explanation: #d/dxsec^2(e^x)=d/dx[sec(e^x)]^2# #=2sec(e^x) * sec(e^x) * tan(e^x) * e^x# 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 3172 views around the world You can reuse this answer Creative Commons License