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)

Question

experimentx · Answer

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'

anonymous · Answer

i got headache with this too ><

experimentx · Answer

apparently you can put f(x,y,z) = some constant ... sill separating x from those values is quite difficult

anonymous · Answer

ooop i forgot 
xz + ylnx + x^2+ 4 = 0

experimentx · Answer

still separating x out of ln(x) is quite a challenge.
while you can do the last part

anonymous · Answer

how can i separate x from lnx
do you have any concept to do that?

experimentx · Answer

the last part requires that ... for separation of x, PDE is the best guess,

experimentx · Answer

apply product rule

anonymous · Answer

xz + ylnx + x^2 + 4 = 0

anonymous · Answer

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

anonymous · Answer

Thank you all for help

experimentx · Answer

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