Need Help with partial derivatives

[Jul.ib]

Hello please if anyone can help me finding a solution for this problem. I would really appreciate it.
We have y function of p and x, x a function of y and p
Given the below derivates we need to find dy/dx

 

[mmm4444bot]

From translate.google.com (symbols edited in; see methods described in the Read Before Posting notice):

E. We consider a variable y that depends on two magnitudes x and p according to the formula:

y = Ψ(x, p)

It is further assumed that the magnitude x is related to p and y in the following way:

x = ϕ(p, y)

Calculate the derivative of y with respect to x as a function of the 4 partial derivatives that are assumed to be known:

∂Ψ/∂x

∂Ψ/∂p

∂ϕ/∂y

∂ϕ/∂p

?

 

[Jul.ib]

Thanks but my problem is not with translation. It's with how to get dy/dx

 

[mmm4444bot]

Thanks but my problem is not with translation … It's with how to get dy/dx

Hi Jul.ib -- I posted the translation for other readers, and I mentioned the guidelines in case you needed ideas for posting symbols.

Tutors would like to see how far you got. Can you post what you've tried or thought about?

\(\;\)

 

[Jul.ib]

dy/ dx = ∂Ψ/∂x
= (∂Ψ/∂p) (∂p/∂x)
= (∂Ψ/∂p) (∂p/∂y) (∂y/∂x)
= (∂Ψ/∂p) (∂p/∂x) (∂x/∂y) (∂y/∂x)
= [(∂Ψ/∂p) (∂ϕ/∂y) (∂Ψ/∂x)] / (∂ϕ/∂p)

I'm sorry if my answer is wrong but that's what I was working on
Thanks