Substitute your functions of p back into the original equation, expand it out and slog through it.
Sometimes with problems like these, you might find that certain things simplify a bit. For example you have a common factor of "p" in each x, y and z functions.
The part that is trickiest is the algebra. When you get to the calculus after the substitution, make sure you know how to do the chain rule
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Partial derivatives
du/dx = 2xy^3
dx/dp = 1+2p
du/dy=3x^2y^2
dy/dp=(p+1)e^p
du/dz=4z^3
dz/dp=sinp + pcosp
then, du/dp = (du/dx)(dx/dp)+(du/dy)(dy/dp)+(du/dz)(dz/dp)=...
Substitute your functions of p back into the original equation, expand it out and slog through it.
Sometimes with problems like these, you might find that certain things simplify a bit. For example you have a common factor of "p" in each x, y and z functions.
The part that is trickiest is the algebra. When you get to the calculus after the substitution, make sure you know how to do the chain rule