1. ## Product rule problem - cannot find answer.

Hey guys, this is likely a really simple problem I have here.

basically my problem is to find the derivative of $\displaystyle \frac {-18}{(x^2 - 9)^2}$

So I make that $\displaystyle (-18)(x^2 - 9)^-2$ so I can use the product rule.

So the derivative of $\displaystyle (x^2 - 9)^ -2)$ is $\displaystyle \frac {2x}{(x^2 - 9)^2}$

I do not know how to find the derivative of -18. I need this derivative to use the product rule, right? I believe it to be 0 or 1... but I have no idea. Please help!

2. Hello buddy.

Originally Posted by Kakariki
Hey guys, this is likely a really simple problem I have here.

basically my problem is to find the derivative of $\displaystyle \frac {-18}{(x^2 - 9)^2}$

So I make that $\displaystyle (-18)(x^2 - 9)^-2$ so I can use the product rule.
I would say you find the derivative of (x^2 - 9)^-2 by using the chain rule

Originally Posted by Kakariki
So the derivative of $\displaystyle (x^2 - 9)^ -2)$ is $\displaystyle \frac {2x}{(x^2 - 9)^2}$
It is not!

let $\displaystyle f(x) := (x^2-9)^{-2}$

Using the chain rule leads to

$\displaystyle f'(x) = -2*2x*(x^2-9)^{-2-1} = -4x*(x^2-9)^{-3}$

Originally Posted by Kakariki
I do not know how to find the derivative of -18. I need this derivative to use the product rule, right? I believe it to be 0 or 1... but I have no idea. Please help!
The derivative of -18 is "0".

If you want to find the derivative of$\displaystyle x^1$ it is $\displaystyle 1* x^{1-1} = 1*x^{0} = 1*1$ by definition, so it is equal to one

-18 has no x in it, so it is a constant -> the derivative of a constant is 0

And in your example you do not need to use the product rule, because -18 is a factor of $\displaystyle (x^2-9)^{-2}$.

So the solution is $\displaystyle -18*[(x^2-9)^{-2}]' = -18 * (-4x*(x^2-9)^{-3})$

You can use the product rule -> but you need to use that [-18]' = 0.

Any more questions?

Rapha

3. That was a rather terrible mistake of mine. I guess I was not thinking when doing the derivative of $\displaystyle (x^2 - 9)^-2$. I thought that the derivative of (-18) would be 0, but it wasn't working out with my answer, and you pointed out why! Thank you very much!