Using chain rule when one of the variables is constant

[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

 

[Office_Shredder]

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.

 

[PandaKitten]

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

 

[PandaKitten]

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

 

[Frabjous]

Would you provide the problem as it was assigned?

 

[PandaKitten]

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

 

[willem2]

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.

 

[Frabjous]

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

 

[PandaKitten]

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?