# Thread: Derivatives - product/quotient/chain rule

1. ## Derivatives - product/quotient/chain rule

It would be greatly appreciated if anyone can provide a detailed solution to finding the derivative of; $(x^2 - 9) sqrt(x+2)$

Thanks in advance!

2. Originally Posted by Archduke01
It would be greatly appreciated if anyone can provide a detailed solution to finding the derivative of; $(x^2 - 9) sqrt(x+2)$

Thanks in advance!
use the product rule ... let's see what you get.

3. I keep getting $[2x(x+2) + (x^2 + 9)] / sqrt (t+2)$.

I need someone to provide steps so I can see where I went wrong.

4. product rule ...

$\frac{d}{dx}(f \cdot g) = fg' + gf'$

$\frac{d}{dx}[(x^2-9)\sqrt{x+2}]$

$(x^2-9) \cdot \frac{1}{2\sqrt{x+2}} + \sqrt{x+2} \cdot 2x$

5. Thanks, I know the product rule - my answer was the simplified version of what that but somewhere in my simplification I went wrong. How do I proceed from what you've posted? Or is that as far as we're supposed to go?

6. Originally Posted by Archduke01
Thanks, I know the product rule - my answer was the simplified version of what that but somewhere in my simplification I went wrong. How do I proceed from what you've posted? Or is that as far as we're supposed to go?
common denominator is $2\sqrt{x+2}$ ... proceed from there.

you should get $\frac{5x^2 +8x - 9}{2\sqrt{x+2}}$