Question: 1 let s be the surface defined by the implicit...

[1] Let S be the surface defined by the implicit equation

x + y + z = sin(xyz) near the origin (x, y, z) = (0, 0, 0).

(1) Put f(x, y, z) = x + y + z − sin(xyz). Calculate the partial derivatives fx, fy and fz at (x, y, z) ∈ $R^3$.

(2) Find the tangent plane and the normal line of the surface S at the origin (x, y, z) = (0, 0, 0).