# Using chain rule when one of the variables is constant

• PandaKitten
In summary, the problem asks you to find E at x = 10cm from a pressure source. You might need to use a numerical method, such as the Taylor expansion, to solve for E.
PandaKitten
Homework Statement
-dE/dx = A*(n/E )*ln(E)
n=P/T
Find dE/dP
Where T and A and dx are constants. E and P are variables
Relevant Equations
-dE/dx = A*(n/E )*ln(E)
n=P/T
So first thing I tried was to separate the variables then differentiate by parts, setting u = E and v = 1/ln(E) (and the other way around) but I couldn't do the integral it gave.
Then I tried to reason that because dx was constants then dE/dx is equal to E/x but I was told that's not the case. The lecturer also mentioned the truncated series for a Taylor expansion but I'm not exactly sure how that is relevant

I'm confused how the thing on the right relates to x. What does it mean for dx to be a constant?

In general if you have ##dE/dx=C## for some constant C, then integrating gives you ##E=Cx+D## for an arbitrary constant ##D##. I can't tell if you're trying to say that's the situation you're in.

The first equation works out the rate of decrease of energy with distance -dE/dx of an energy emitter. But in this question, we are at a fixed distance from the energy emitter. So it wants us to write it in terms of dE/dP instead where P is pressure (second equation). Let me know if it is still unclear. Sorry if this doesn't make sense

We're at a fixed distance from the emitter so dx is constant**

Would you provide the problem as it was assigned?

The question sheet includes a lot of background information and other questions. Below is a summary.

You'll need to solve a differential equation for E and x to compute E at x = 10.
You might need a numerical method for this. The Taylor expansion could also be used here (if the error is small enough). This E will of course depend on P, so you can calculate dE/dP. This might have to be done numerically also.

Be careful, when E gets small enough, the ln changes sign, so there is something else that has to be brought in.

willem2 said:
You'll need to solve a differential equation for E and x to compute E at x = 10.
You might need a numerical method for this. The Taylor expansion could also be used here (if the error is small enough). This E will of course depend on P, so you can calculate dE/dP. This might have to be done numerically also.
How would I solve it using the Taylor expansion? Would I use this formula and set X= 10cm?

## What is the chain rule?

The chain rule is a mathematical rule used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

## When should the chain rule be used?

The chain rule should be used when finding the derivative of a function that is composed of two or more functions. It is particularly useful when one of the variables is dependent on another variable.

## How is the chain rule applied when one variable is constant?

When one variable is constant, it can be treated as a coefficient and brought outside of the derivative. The derivative of the remaining variable can then be found using the chain rule as usual.

## Can the chain rule be used for functions with more than two variables?

Yes, the chain rule can be applied to functions with any number of variables. Each variable would be treated as a separate function and the chain rule would be applied to each one.

## Are there any common mistakes when using the chain rule with a constant variable?

One common mistake is forgetting to bring the constant variable outside of the derivative. Another mistake is incorrectly applying the chain rule to the remaining variable. It is important to carefully follow the steps of the chain rule to avoid these mistakes.

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