Find the two first-order partial derivatives of z with respect to x and y
when z = z(x, y) is defined implicitly by
z*(e^xy+y)+z^3=1.
I started by multiplying the brackets out to give; ze^xy + zy + z^3 - 1 = 0
i then differentiated each side implicitly and got;
dz/dx = yze^xy
and...