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 1399 views around the world You can reuse this answer Creative Commons License