Given:

$\displaystyle

f(x) = \frac{x^2}{x^2 + 4}

$

Using the quotient rule, I found that:

$\displaystyle

f'(x) = \frac{8x}{(x^2 + 4)^2}

$

$\displaystyle

f''(x) = \frac{-8(3x^4 + 8x^2 - 16)}{(x^2 + 4)^4}

$

Is this correct? I am a little suspicious of $\displaystyle f''(x)$. It seems to be a little too big, but I can't seem to find any mistake in my work.