Question

Calculate first order partial derivatives of a function $z = x^{2}y - 4x\sqrt{y} - 6y^{2} + 5$ at the point M(2;1)

Answer 1

$z_x=2xy-4\sqrt{y}$

$z_x(2,1)=2\cdot2-4\sqrt{1}=0$

$z_y=x^2-2x/\sqrt{y}-12y$

$z_y(2,1)=2^2-2\cdot2-12=-12$