How do you differentiate #y=x^3/(1-x^2)#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lithia Feb 20, 2017 #(x^2(3-x^2))/(1-x^2)^2# Explanation: #y=x^3/(1-x^2)# find the derivative using the Quotient Rule # y'=(f'(x)g(x)-f(x)g'(x))/[g(x)]^2# when #f(x)=x^3# and #g(x)=1-x^2# #y'=((x^3)'(1-x^2)-(x^3)(1-x^2)')/[(1-x^2)]^2# #y'=((3x^2)(1-x^2)-(x^3)(-2x))/[(1-x^2)]^2=(3x^2-3x^4+2x^4)/(1-x^2)^2=(-x^4+3x^2)/(1-x^2)^2=(x^2(3-x^2))/(1-x^2)^2# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 18577 views around the world You can reuse this answer Creative Commons License