the question im having trouble with is
$\displaystyle f(x) = \frac{\sqrt{5x}(1+x^2)}{\sqrt{2}}$
is there a simpler way than using the quotient rule? itried that, but ended up with a ridiculously long answer for the derivative.
You are supposed to use the product rule here. $\displaystyle \frac{1}{\sqrt{2}}$ is a constant. So you have to find the derivative this way:
$\displaystyle \frac{1}{\sqrt{2}} \times \frac{d}{dx}\sqrt{5x}(1+x^2)$
or,
$\displaystyle \frac{\sqrt{5}}{\sqrt{2}} \times \frac{d}{dx}\sqrt{x}(1+x^2)$
Are you comfortable with the product rule. Try it and post if you have problems