Hi!

I just started learning calculus this semester and it's a total brainbreak. We are on derivatives now and we just had a quiz about derivatives and limits. The problem is, when I thought I already knew derivatives I felt stupid during the whole 3 hours of answering the quiz. I found out I couldn't work on the complicated equations (especially the ones with the bar lines and radical signs) using the method our instructor taught us. I ended up having answered only one item which was a limit problem. Then a senior told me that I should have used the theorems for derivatives (not sure how to call that).

Here's one from our quiz:

$\displaystyle y=(1+3x-x^2)(x^2-5)$

$\displaystyle \frac {dy}{dx} = (x^2-5) \frac {d}{dx} (1+3x-x^2) + (1+3x-x^2) \frac {d}{dx} (x^2-5)$

$\displaystyle \frac {dy}{dx} = (x^2-5) [ \frac {d}{dx} (1) + \frac {d}{dx}(3x) + \frac {d}{dx} (x^2) ] + (1+3x-x^2) [ \frac {d}{dx} (x^2) - \frac {d}{dx}(5) ] $

$\displaystyle \frac {dy}{dx} = (x^2-5) (3+2x) + (1+3x-x^2) (2x)$

$\displaystyle \frac {dy}{dx} = 2x^3 + 3x^2 - 10x - 15 - 2x^3 + 6x^2 +2x$

$\displaystyle \frac {dy}{dx} = 9x^2 - 8x - 15$

Is my answer correct? Unfortunately I can no longer get any mark for getting it right so it's good as incorrect.

Thanks in advance!