How do you differentiate #f(x)=sec^4(x^3-x^2 ) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Bdub Nov 1, 2016 #f'(x)=4(3x^2-2x)sec^4(x^3-x^2)tan(x^3-x^2)# Explanation: #f(x)=sec^4(x^3-x^2)=(sec(x^3-x^2))^4# #f'(x)=4(sec(x^3-x^2))^3*sec(x^3-x^2))tan(x^3-x^2)*(3x^2-2x)# #f'(x)=4(3x^2-2x)sec^4(x^3-x^2)tan(x^3-x^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 1110 views around the world You can reuse this answer Creative Commons License