Differential equation homework question

[yonathan]

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

 

[Hootenanny]

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

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.

 

[yonathan]

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 derivative of P=Po e^-h/c? pls?

 

[Hootenanny]

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 derivative of P=Po e^-h/c? pls?

Notice that the two derivatives that you have found are not equivalent:

P=C*Po e^-h or P=Po*(-h/c) e^-h/c

So, which one is it?

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

 

[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.

 

[jeffreydk]

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

 

[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?

 

[yonathan]

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

 

[Defennder]

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

 

[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??

 

[Hootenanny]

the derivative of e^f(x) is (f)e^f(x)

Are you sure about that?

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

Simply let:

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

Then you have:

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

As above.

 

[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.

 

[Hootenanny]

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.

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

 

[yonathan]

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

 

[Hootenanny]

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

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?

 

[yonathan]

sorry i still don't follow, can u explain it to me in another way or something? i don't 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?

 

[Hootenanny]

sorry i still don't follow, can u explain it to me in another way or something? i don't 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?

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

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

What does it represent?

 

[yonathan]

it represents the differentiation of P which is P.

 

[Hootenanny]

it represents the differentiation of P which is P.

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

 

[yonathan]

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

 

[Defennder]

That's what you're supposed to figure out. How do you differentiate an exponential function? Read it up on Wikipedia:
http://en.wikipedia.org/wiki/Exponential_function#Derivatives_and_differential_equations
http://en.wikipedia.org/wiki/Table_of_derivatives