How do you differentiate y=x^3/(1-x^2)?

1 Answer
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