Given xz + ylnx + x^2 + 4 define x as differentiable function of two independent variable y and z. Find the value of dx/dz at point (x, y, z) = (1, -1, 3)

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Given xz + ylnx + x^2 + 4 define x as differentiable function of two independent variable y and z. Find the value of dx/dz at point (x, y, z) = (1, -1, 3)

Differential Equations
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There are three independent variables given that f(x,y,z) = xz + ylnx + x^2 + 4 how do you intent to define x and function of independent variable 'x' and 'y'
i got headache with this too ><
apparently you can put f(x,y,z) = some constant ... sill separating x from those values is quite difficult

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Other answers:

ooop i forgot xz + ylnx + x^2+ 4 = 0
still separating x out of ln(x) is quite a challenge. while you can do the last part
how can i separate x from lnx do you have any concept to do that?
the last part requires that ... for separation of x, PDE is the best guess,
apply product rule
xz + ylnx + x^2 + 4 = 0
about find the value in the last part i know how to solve it, but about define x as differentiable function of two independent variable y and z i still not clear
Thank you all for help
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