# Differential equation homework question

1. Jul 14, 2008

### yonathan

can u pls help me with this quaestion???
p=Po e^-h/c

2. Jul 14, 2008

### Hootenanny

Staff Emeritus
Re: Differential Equation homework help

Welcome to PF yonathan,

Please post your question exactly as it is stated in your text/homework sheet together with all relevant information and your initial attempts to solve the problem.

Once you have done this, someone will be more than happy to help.

3. Jul 15, 2008

### yonathan

Re: Differential Equation homework help

the pressure P of the atmosphere at height 'h' above ground level is given by P=Po e^-h/c where Po is the pressure at ground level and c is the constant.determine the rate of change of pressure with height when Po=1.013*10^5 pascals C=6.05*10^4 at 1450 meters.
i used the for differentiation to differentiate it and find the first derivative of P=Po e^-h/c and i got P=C*Po e^-h or P=Po*(-h/c) e^-h/c and i substitute ted the numbers the given and my calculator seems not to find the ans for it. so can u help me find the derivitive of P=Po e^-h/c? pls?

4. Jul 15, 2008

### Hootenanny

Staff Emeritus
Re: Differential Equation homework help

Notice that the two derivatives that you have found are not equivalent:
So, which one is it?

You should also use correct notation: P' instead of P.

5. Jul 15, 2008

### yonathan

the reason put or (where u quoted it at the end of ur message) was to ask u which of the answers i came up with was the correct one.

6. Jul 15, 2008

### jeffreydk

You want to find $$\frac{dp}{dh}$$ where $$c$$ and $$p_0$$ are constant. How would you differentiate $$\frac{d}{dh}(p_0e^{\frac{-h}{c}})$$?

7. Jul 15, 2008

### yonathan

that was wat i was tyin to find,but i am not sure. i came with the answers i showed u where i added 'or' (the one u put at the end of ur message before this message) and i don't think it is wright, do u think it was right???

8. Jul 15, 2008

### yonathan

what jeffreydk wrote is what i want to figure out exactly, if you can help in that it would be very helpful.

9. Jul 15, 2008

### Defennder

You just need to know how to differentiate e^f(x). What is the derivative of that?

10. Jul 16, 2008

### yonathan

the derivative of e^f(x) is (f)e^f(x) but what if it was e^(F/x) that's what i want to find out??

11. Jul 16, 2008

### Hootenanny

Staff Emeritus
Simply let:

$$f(h) = \frac{-h}{c}$$

Then you have:

$$P = P_0e^{f(h)}$$

As above.

12. Jul 16, 2008

### yonathan

so the first derivative of Po e^-h/c is dp/dh=Poe^f(h), where f(h)is -h/c, and after this, all i have to do is substitute the numbers given, yeh? and i am sure about the derivative u asked me.

13. Jul 17, 2008

### Hootenanny

Staff Emeritus
No it isn't, you need to recheck you derivative. Use the chain rule.

14. Jul 17, 2008

### yonathan

what is 'f' in ur chain rule cause according to it the derivative is f(h)is -h/c??

15. Jul 17, 2008

### Hootenanny

Staff Emeritus
Note that in this case, h is a variable and not constant. The chain rule states that for a composite function $y\left(f(x)\right)$

$$\frac{dy}{dx} = \frac{dy}{df}\frac{df}{dx}$$

So in your case we have:

$$P = P_0e^{f(h)}$$

$$\frac{d}{dh}P = P_0\frac{df}{dh}e^{f(h)}$$

Do you follow?

16. Jul 20, 2008

### yonathan

sorry i still don't follow, can u explain it to me in another way or something??? i dont know wat to do with the last answer u gave me. do i substitute my numbers on ur answer and wat is e^f(h), how am i suppose to solve it???

17. Jul 20, 2008

### Hootenanny

Staff Emeritus
Okay, let's take this a term at a time. What is:

$$\frac{d}{dh}P$$

What does it represent?

18. Jul 20, 2008

### yonathan

it represents the differentiation of P which is P.

19. Jul 20, 2008

### Hootenanny

Staff Emeritus
It represents the derivative of P with respect to h, which is not P.

20. Jul 20, 2008

### yonathan

so what is d/dh of e^-h/c