Let z {\displaystyle \displaystyle z} be defined implicitly by x 2 z 3 + y sin ( π x ) = − y 2 {\displaystyle \displaystyle x^{2}z^{3}+y\sin(\pi x)=-y^{2}} . Find ∂ z ∂ x {\displaystyle \displaystyle {\frac {\partial z}{\partial x}}} at the point P = ( 1 , 1 , − 1 ) {\displaystyle \displaystyle P=(1,1,-1)} .
