What is the derivative of Find (x^3 + 1) / (1- 2x^2 )

We find the derivative of the expression using the
quotient rule.

Now for finding the derivative of f(x)/g(x)
the quotient rule is [f’(x) g(x) – f(x) g’(x)]/ [g(x)]
^2

Here f(x) = x^3+1. So we have f’(x)
3x.

g(x) = 1- 2x^2,  so g’(x) =
-4x

Therefore the derivative of (x^3 + 1) / (1 - 2x^2 )
is

[(1- x^2)  * 3x – (-4x) * (x^3 +1)] / (1- 2x^2)
^2

=> [(1- x^2)  * 3x + 4x * (x^3 +1)] / (1- 2x^2)
^2

=>  [3x - 3x^3 + 4x^4 + 4x] / (1- 2x^2)
^2

=> [ 4x^4 - 3x^3 + 7x] / (1- 2x^2)
^2

=> x*(4x^3 - 3x^2 +7) / (1-
2x^2)^2

Therefore the required result is
x*(4x^3 - 3x^2 +7) / (1- 2x^2)^2