How do you differentiate #f(x)=sqrt(xsin(ln(x)^3)# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Gerardina C. Jan 25, 2017 #(sinlnx^3+3coslnx^3)/(2sqrt(xsinlnx^3))# Explanation: #f'(x)=1/(2sqrt(xsinlnx^3))*(1*sinlnx^3+cancelx*coslnx^3*1/cancel(x^3)*3cancel(x^2))# #=(sinlnx^3+3coslnx^3)/(2sqrt(xsinlnx^3))# 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 1482 views around the world You can reuse this answer Creative Commons License