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 18984 views around the world You can reuse this answer Creative Commons License