How do you differentiate #f(x)=(4x^6-3sqrt(x/(x-5)^2)+2)^2# using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Sonnhard Jun 23, 2018 #f'(x)=2(4*x^6-3sqrt(x/(x-5)^2)+2)*(24*x^5-3/(2*sqrt(x/(x-5)^2))((-x-5)/(x-5)^3))# Explanation: By the chain rule we get #f'(x)=2(4x^6-3sqrt(x/(x-5)^2)+2)*(24*x^5-3/(2*sqrt(x/(x-5)^2))*(x-5-2x)/(x-5)^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 1408 views around the world You can reuse this answer Creative Commons License