How do you differentiate #f(x) = sqrt(arctan(2x^3) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer sankarankalyanam Nov 11, 2017 #f’(x) = (3x^2) / ((1+4x^6)(sqrt(arctan(2x^3)))# Explanation: #f(x) = sqrt(arctan(2x^3))# #f’(x) = (1/(2sqrt(arctan(2x^3))) * 1/(1+(2x^3)^2) * (6x^2))# # = (3x^2) / ((1+4x^6)(sqrt(arctan(2x^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 1234 views around the world You can reuse this answer Creative Commons License