# Thread: Product and Quotient Rule with Derivatives

1. ## Product and Quotient Rule with Derivatives

The problem is:
F(x) = ((1/y^2) - (2/y^4)) (y + 8y^3)

I can find derivatives from other functions, but my professor has neglected to tell us how to do it with functions like this. I have tried this problem many times, with varying answers: It is so frustrating. I have used the product rule right away, or I have multiplied it out first and then used to power rule to find f'(x), but I keep getting the wrong answer. Please explain how to get the right answer and walk me through the question step by step. Thank you so much.

2. $\displaystyle f(x) = (\frac{1}{y^2} - \frac{2}{y^4})(y + 8y^3)$

$\displaystyle =(y^{-2}-2y^{-4})*(y+8y^3)$

$\displaystyle =y^{-1}+8y-2y^{-3}+16y^{-1}$

Well now you can use power rule on this:

So $\displaystyle f'(x)=(-1)*y^{-1-1}+8-2*(-3)y^{-3-1}+16*(-1)y^{-1-1}$

$\displaystyle =-y^{-2}+6y^{-4}-16y^{-2}+8$

oh crap I misread a parenthesis. (fixing that now)

There that's it.