How do you differentiate #f(x)=sece^(4x)# using the chain rule.? Calculus Basic Differentiation Rules Chain Rule 1 Answer Trevor Ryan. Feb 12, 2016 #f'(x)=4e^(4x)sec(e^(4x)) * tan(e^(4x))# Explanation: By the chain rule, if #y=f(u) and u=f(x)#. then #dy/dx=(dy)/(du)*(du)/dx# #therefored/dx[sec(e^(4x))]=sec(e^(4x)) * tan(e^(4x)) * e^(4x) * 4# 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 1331 views around the world You can reuse this answer Creative Commons License