How do you differentiate #f(x) = x/sqrt(sin^2(1+x^2) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Bdub Nov 1, 2016 #f'(x)=(sin(1+x^2)-2x^2cos(1+x^2))/sin^2(1+x^2)# Explanation: #f(x)=x/(sqrt(sin^2(1+x^2))# Use quotient rule and chain rule #f=x, g=((sin(1+x^2))^2)^(1/2) = sin(1+x^2)# #f'=1, g'=cos(1+x^2)*2x# #f'(x)=(gf'-fg')/g^2# #f'(x)=(sin(1+x^2)-2x^2cos(1+x^2))/sin^2(1+x^2)# 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 1370 views around the world You can reuse this answer Creative Commons License