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# Partial derivative watch

1. Anyone have any good resources on partial derivatives? - for someone who has never done it before. Thanks

If not please could someone explain the basic concepts?
2. It's when you have a multivariable function but you take the derivative with respect to one variable. You basically treat the other variables as constants.

https://www.youtube.com/watch?v=SbfRDBmyAMI

https://www.khanacademy.org/math/mul...al-derivatives
3. (Original post by thekidwhogames)
It's when you have a multivariable function but you take the derivative with respect to one variable. You basically treat the other variables as constants.

https://www.youtube.com/watch?v=SbfRDBmyAMI

https://www.khanacademy.org/math/mul...al-derivatives
Thanks ill take a look
4. (Original post by thekidwhogames)
It's when you have a multivariable function but you take the derivative with respect to one variable. You basically treat the other variables as constants.

https://www.youtube.com/watch?v=SbfRDBmyAMI

https://www.khanacademy.org/math/mul...al-derivatives
So is second partial derivative basically differentiating twice?

For example (original expression V = RT/P) if the first derivative was (dV/dT)p = R/P then would the second derivative be (dV^2/d^2T)p = 0
5. (Original post by kiiten)
So is second partial derivative basically differentiating twice?

For example (original expression V = RT/P) if the first derivative was (dV/dT)p = R/P then would the second derivative be (dV^2/d^2T)p = 0
This is fine apart from the fact that you have on the LHS for some reason. It shouldn't be there.

Furthermore, you want to say when talking about partial derivatives, instead of . I understand it's easier to just use 'd' on TSR if you don't know how to write the other one, so that's fine, though also note that we have the notation of for and , respectively. And similalrly,
6. (Original post by RDKGames)
This is fine apart from the fact that you have on the LHS for some reason. It shouldn't be there.

Furthermore, you want to say when talking about partial derivatives, instead of . I understand it's easier to just use 'd' on TSR if you don't know how to write the other one, so that's fine, though also note that we have the notation of for and , respectively. And similalrly,
Sorry i made a mistake - the equation is RT/p the p on the LHS shows that p is a constant (my lecture notes say this is how you should write it?).

Yes i meant the the other type of d. Oh so in my case would it be (dV/dT)p x (dV/dp)T to get the second derivative? Although the question suggests i should have more than 1 second derivative as the answer??
7. (Original post by kiiten)
Sorry i made a mistake - the equation is RT/p the p on the LHS shows that p is a constant (my lecture notes say this is how you should write it?).

Yes i meant the the other type of d. Oh so in my case would it be (dV/dT)p x (dV/dp)T to get the second derivative? Although the question suggests i should have more than 1 second derivative as the answer??
Er... not sure what your lecture notes are saying about that as it doesn't seem right. Posting the full question might help understand what's going on.

8. (Original post by RDKGames)
Er... not sure what your lecture notes are saying about that as it doesn't seem right.

in some notes it has a small subscript letter to represent whats constant outside of the brackets of a partial derivative, im pretty sure its just an obscure piece of notation not many people use
9. (Original post by bruh2132)
in some notes it has a small subscript letter to represent whats constant outside of the brackets of a partial derivative, im pretty sure its just an obscure piece of notation not many people use
Could be - I certainly never came across it, only the usual subscript to denote the variable to which we differentiate with respect to.

I'd hate to use their notation for functions of 4 or more variables!
10. (Original post by kiiten)
Anyone have any good resources on partial derivatives? - for someone who has never done it before. Thanks

If not please could someone explain the basic concepts?
theres also https://courses.maths.ox.ac.uk/overview/undergraduate on the introductory calculus but it gets pretty annoying to understand near the chain rule. but there are notes and question papers
11. (Original post by RDKGames)
Could be - I certainly never came across it, only the usual subscript to denote the variable to which we differentiate with respect to.

I'd hate to use their notation for functions of 4 or more variables!
Yup, I can't imagine how it would get past two, just listing variables in subscript would look horrible
12. (Original post by RDKGames)
Could be - I certainly never came across it, only the usual subscript to denote the variable to which we differentiate with respect to.

I'd hate to use their notation for functions of 4 or more variables!
(Original post by bruh2132)
in some notes it has a small subscript letter to represent whats constant outside of the brackets of a partial derivative, im pretty sure its just an obscure piece of notation not many people use
Yes its just a small subscript to that tells you what variables are constant. I actually find it quite helpful

Ive attached the original question. Q3 is what ive already calculated. The notation for Q4 confused me and Q5 is what i was asking about the second partial derivative. NOTE: I wrote V instead of Vm just because its easier here.

Attachment 722980722984
Attached Images

13. (Original post by kiiten)
Yes its just a small subscript to that tells you what variables are constant. I actually find it quite helpful
The only two issues I have with it is that (a) why do we not mention R being a constant as well within the subscript...? and (b) it would get very messy for more variables.

(Original post by kiiten)
Ive attached the original question. Q3 is what ive already calculated. The notation for Q4 confused me and Q5 is what i was asking about the second partial derivative. NOTE: I wrote V instead of Vm just because its easier here.
For Q4, just differentiate both sides w.r.t P

For Q5, just take the expressions you found in Q2 and differentiate both w.r.t to the other variable.
14. (Original post by RDKGames)
The only two issues I have with it is that (a) why do we not mention R being a constant as well within the subscript...? and (b) it would get very messy for more variables.

For Q4, just differentiate both sides w.r.t P

For Q5, just take the expressions you found in Q2 and differentiate both w.r.t to the other variable.
Good point! Maybe the person who made the questions made a mistake?

For Q4 I dont understand what im differentiating
15. (Original post by kiiten)
Good point! Maybe the person who made the questions made a mistake?

For Q4 I dont understand what im differentiating
Both sides of that equation w.r.t P. The LHS will give and the RHS will give something else, and that answers the question.
16. (Original post by RDKGames)
Er... not sure what your lecture notes are saying about that as it doesn't seem right. Posting the full question might help understand what's going on.

Hey im getting a bit confused with the notation.

So i have 2 first order derivatives and tried to calculate the 2 second order. Is my notation/answer correct?

Sorry i had to do it on paint so it was easier to see

17. (Original post by kiiten)
Hey im getting a bit confused with the notation.

So i have 2 first order derivatives and tried to calculate the 2 second order. Is my notation/answer correct?

Sorry i had to do it on paint so it was easier to see
Yes these are correct.

I had initially misinterpreted Q5 as it seemed to me as if they wanted something of the same form as in Q4, but guess not.

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