Suppose That the Equation $F ( x , y , z ) = 0$

Essay

Suppose that the equation $F ( x , y , z ) = 0$ defines $Z$ implicitly as a function of $x$ and $y$ . Let $( a , b , c )$ be a point such that $F ( a , b , c ) = 0$ and $\nabla F ( a , b , c ) = ( 2 , - 3,4 )$ . Find $\frac { \delta z } { \delta x } ( a , b )$ and $\frac { \delta z } { \delta y } ( a , b )$ .