Consider the function $f(x,y) = (x^2+y^3)^{1/4}$.
The equation of the tangent plane at $x_0=4,y_0=0,z_0=2$ is: $z -z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)$