# Aerospace Math help

1. Jul 25, 2009

### mfc5200

Can someone please explain the steps to derive this? I've seen it everywhere, but the explanation is never given.

My confusion arises from the second line. In EVERY math book I've ever picked up, whenever you take a derivative, it is ALWAYS with respective to something, i.e y w.r.t x, or some variable w.r.t time, etc. But in this example as shown in textbooks, it seems as though they are taking a derivative, but it is not w.r.t anything. For example, instead of saying dy/dx, they would just be saying dy, which doesn't really make any sense to me. I'm confused about this.

I haven't seen a good explanation of this type of derivative yet. I attached an example. Thanks

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• ###### eq.png
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2. Jul 25, 2009

### Cyrus

It's just a differential area. You have not paid close enough attention to your math books.

Last edited: Jul 25, 2009
3. Jul 26, 2009

### FredGarvin

Look up the product rule for derivatives. The dot implies the time derivative. Since all terms on both sides are wrt dt it cancels out.

4. Jul 26, 2009

### apc3161

Could you maybe say a little bit more about that. I think this is the part that is confusing me.

5. Jul 26, 2009

### Cyrus

It's a differential, it's not a derivative.

6. Jul 26, 2009

### tiny-tim

Hi mfc5200!

Does this help … http://en.wikipedia.org/wiki/Differential_(infinitesimal) ?

7. Jul 26, 2009

### Bob S

Suppose

m-dot =pVA
then
d(m-dot)/dt = pV dA/dt + VA dp/dt + pA dV/dt
Now multiply both sides by dt.

8. Jul 30, 2009

### mfc5200

Yea, I was able to get that far. I just wasn't sure if you were "allowed" to do that. I've never seen that done before.

9. Jul 30, 2009

### Cyrus

You're not always allowed to do this. So, be aware of that.