Homework Soursefind zx and zy as functions of x y and z assuming that the f
find ?z/?x and ?z/?y as functions of x, y, and z, assuming that the function z=f(x,y) is given implicitly by the equation 2(z^3) - xyz = xy.
Solution
2z^3 - xyz = xy
differentiating w.r.t x partially keeping y constant
==> 6Z^2 * Zx - yz - xyZx = y
==> Zx = (y+yz)/(6z^2 - xy)
w.=r.t y
==> 6Z^2 * Zy - xz - xyZy = x
Zy = (x+xz)/(6z^2 - xy)
