How do you find the derivative of # f(x) = sin ^{ 3 }x# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Michael Nov 22, 2015 #f'(x)=3sin^2xcosx# Explanation: #f(x)=sin^3x# Apply the power rule to #sin^3x# and then multiply by the derivative of #sinxrArr# #f'(x)=3sin^2xcosx# 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 1183 views around the world You can reuse this answer Creative Commons License