Question

Let the surface z = f(x, y) be defined implicitly by the equation: sin(xyz) = x2y2 + z2 − 1 .

(a). Find the partial derivatives ∂ z / ∂ z & ∂x/ ∂y

(b). Find the equation of the tangent plane at the point (1, 1, 0).

(c). In which direction does f increase most rapidly at this point?