Question

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

Answer 1

`(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`