Question

What is the second derivative of `f(x)=x^2/(x+3)`?

Answer 1

Differentiate once, and then differentiate again.

By the quotient rule:

`f'(x) = (2x(x + 3) - x^2(1))/(x + 3)^2`

`f'(x) = (2x^2 + 6x - x^2)//(x + 3)^2`

`f'(x) = (x^2 + 6x)/(x^2 + 6x + 9)`

Differentiate once more.

`f''(x) = ((2x + 6)(x^2+ 6x + 9) - ((2x + 6)(x^2 + 6x)))/(x^2 + 6x + 9)^2`

You can simplify this further, but I'll leave the algebra up to you.

Hopefully this helps!