## Basic qns on partial derivatives

1. The problem statement, all variables and given/known data

1. Is (∂P/∂x)(∂x/∂P) = 1?

I realized that's not true, but i'm not sure why.

2. Say we have an equation PV = T*exp(VT)

The question wanted to find (∂P/∂V), (∂V/∂T) and (∂T/∂P) and show that product of all 3 = -1.

3. The attempt at a solution

I tried moving the variables about then differentiate but I got all the wrong answers, for example:

V = (T/P) * exp (VT)

then to find (∂V/∂T) with P constant, i did product rule.. which gave me wrong answers

T = PV * exp(-VT)

then to find (∂T/∂P) with V constant, i use product rule again..which completely gave me the wrong answers..

So I thought that you're not allowed to move the variables around?

Strangely I got (∂P/∂V) correct despite moving the variables around... coincidence?
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 update: i realized its the same! but this way it took much much longer than the solution which they simply took the "ln" throughout to simplify..

Recognitions:
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 Quote by unscientific 1. The problem statement, all variables and given/known data 1. Is (∂P/∂x)(∂x/∂P) = 1? I realized that's not true, but i'm not sure why. 2. Say we have an equation PV = T*exp(VT) The question wanted to find (∂P/∂V), (∂V/∂T) and (∂T/∂P) and show that product of all 3 = -1. 3. The attempt at a solution I tried moving the variables about then differentiate but I got all the wrong answers, for example: V = (T/P) * exp (VT) then to find (∂V/∂T) with P constant, i did product rule.. which gave me wrong answers T = PV * exp(-VT) then to find (∂T/∂P) with V constant, i use product rule again..which completely gave me the wrong answers.. So I thought that you're not allowed to move the variables around? Strangely I got (∂P/∂V) correct despite moving the variables around... coincidence?
Show what you did: you said " ... then to find (∂V/∂T) with P constant, i did product rule.. which gave me wrong answers...". What did you get, and how do you know the answer is wrong?

RGV

## Basic qns on partial derivatives

 Quote by Ray Vickson Show what you did: you said " ... then to find (∂V/∂T) with P constant, i did product rule.. which gave me wrong answers...". What did you get, and how do you know the answer is wrong? RGV
I worked it out finally. It comes out the same as the solutions, so i'm relieved. But can anyone answer the first qn?
 I don't have a clear understanding of partial derivative but the following hint may help you: Suppose P is a function of x and y, we can write $\frac{\partial P}{\partial P}=1$ using chain rule: $\frac{\partial P}{\partial x}\frac{\partial x}{\partial P}+\frac{\partial P}{\partial y}\frac{\partial y}{\partial P}=1$ Due to the second term $\frac{\partial P}{\partial x}\frac{\partial x}{\partial P}≠1$

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