Tangent plane at a surface

Question

Find an equation of the tangent plane to the given surface at the point P(2,0). f(x,y) = (x^2)(e^(xy)).

Answer 1

z = f(x,y) = x²e^xy; P(2,0) z(2, 0) = 4.

z_x = 2xe^xy + x²ye^xy; z_x(2,0) = 4; z_y = x³e^xy; z_y(2, 0) = 8;

Equation of tangent plane: 4(x - 2) + 8(y - 0) - (z - 4) = 0; 4x + 8y - z - 4 = 0