# Stuck getting derivative when can't isolate my variable

1. Feb 28, 2015

### Jon9992

Hi. This is not a homework assignment. I am working to get an extrema on a graph that involves a bunch of functions and got stuck on one step:

How to get the derivative of:
$$\frac{dy}{dn} = \frac{nc(a+b)}{nc+a}$$

I can't get "n" in a place where I recognize how to get the derivative of it. I get stuck here after the first step..
$$nc(a+b)*(nc+a)^{-1}$$

or do I use the quotient rule where it ends up:
$$\frac{[nc(a+b)]'*(nc+a) - nc(a+b)(nc+a)'}{(nc+a)^2}$$
$$\frac{c(a+b)*(nc+a) - nc(a+b)(c)}{(nc+a)^2}$$ ??

Last edited: Feb 28, 2015
2. Feb 28, 2015

### Staff: Mentor

In other words, you want $\frac{d^2 y}{dn^2}$, right? That is, the derivative, with respect to n, of dy/dn.
Since you are differentiating with respect to n, then the derivative of n (with respect to n) is just 1. $\frac{d}{dn}(n) = 1$.
You can use either the product rule (that you started with, above) or the quotient rule - your call. The product rule is usually easier to apply.
I'm not sure I understood what you were asking. If what I wrote isn't what you're looking for, please clarify your question.

3. Feb 28, 2015

### Jon9992

Hi. Thanks. I'm not quite sure what you meant about the d squared y over d n squared. But it sounds like my quotient math above was correct. I wasn't sure if that was right at all.

4. Feb 28, 2015

### Jon9992

Actually. I think I know what you meant. I think I wrote that wrong. I meant $$y=\frac{nc(a+b)}{nc+a}$$

5. Feb 28, 2015

### Staff: Mentor

So all is good, right? You can use either the product rule or the quotient rule for this problem.

I prefer the Leibniz notation for problems like this, rather than the Newton notation. IOW, I prefer d/dn[nc + a] over (nc+a)′, as it isn't clear in the latter notation that you are differentiating with respect to n.