Derivation

[derek784]

Hello, I've got a question like this:

The atmospheric pressure at an altitude of x kilometers above sealevel is approximately e^(−x/8) millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when the altitude of the rocket is 64 kilometers?

Don't you simply derive e^(-x/8) and then plug in x=64? I just want to make sure. But in that case, the "rate of 8 kilometers per second" part of the question is useless?

through chain rule, i got -1/8e^(-x/8). plugging in 64 gets me -1/8e^(-8).

 

[Dr.Peterson]

The atmospheric pressure at an altitude of x kilometers above sealevel is approximately e^(−x/8) millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when the altitude of the rocket is 64 kilometers?

Don't you simply derive e^(-x/8) and then plug in x=64? I just want to make sure. But in that case, the "rate of 8 kilometers per second" part of the question is useless?

through chain rule, i got -1/8e^(-x/8). plugging in 64 gets me -1/8e^(-8).

The derivative of the pressure with respect to x is the rate of change, not in millibars per second, but in millibars per kilometer.

This is a related rates problem! There are three quantities: pressure P, altitude x, and time t. You need to bring time into your work, and that is where the 8 km/s comes in.

You are given that P = e^(−x/8), and that dx/dt = 8. You want to find dP/dt when x = 64. What do you do?

 

[WilliamPounds]

Hello, I've got a question like this: [Moved from a different thread]

The atmospheric pressure at an altitude of x kilometers above sealevel is approximately e^(−x/8) millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when the altitude of the rocket is 64 kilometers?

Don't you simply derive e^(-x/8) and then plug in x=64? I just want to make sure. But in that case, the "rate of 8 kilometers per second" part of the question is useless?

through chain rule, i got -1/8e^(-x/8). plugging in 64 gets me -1/8e^(-8).

 

[Dr.Peterson]

Why have you resubmitted, word for word, the following question, under a different name? [Moved from a different thread]

Derivation

Hello, I've got a question like this: The atmospheric pressure at an altitude of x kilometers above sealevel is approximately e^(−x/8) millibars. A rocket is rising at a rate of 8 kilometers per second vertically. At what rate is the atmospheric pressure changing (in millibars per second) when...

www.freemathhelp.com

Look there for my answer. Also, please observe that the verb is not "derive" but "differentiate". The result is called the "derivative".