Question

Find the value of 𝜕z/𝜕x and 𝜕z/𝜕y at the point (1,1,1) for the surface xy +z3x−2yz = 0 by differentiating implicitly.

Answer 1

z = xy +z³−2yz = 0

$\partial z/ \partial x = y+ z^3$

at point (1,1,1)

$\partial z/ \partial x$ = 1 + 1³ = 2

$\partial z/ \partial y = x +2z$

at point 1,1,1

$\partial z/ \partial y$ = 1 + 2*1 = 3