How do you differentiate #f(x)=root4(1+2x+x^3)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Ananda Dasgupta Apr 5, 2018 # (2+3x^2)/(4(1+2x+3x^2)^{3/4})# Explanation: #f(x)=root4(1+2x+x^3) implies# #(df)/dx = 1/4 (1+2x+x^3)^{1/4-1}times d/dx (1+2x+x^3)# #qquad = (2+3x^2)/(4(1+2x+3x^2)^{3/4})# 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 2443 views around the world You can reuse this answer Creative Commons License