Answer
$-2$
Work Step by Step
In order to find the partial derivative, we will implicitly differentiate with respect to $x$. In doing so, we will treat $y$ as an integer.
x + (z^3 + 3z^2x{\partial z}/{\partial x}}) - 2y{\partial z}/{\partial x}} = 0
at (x,y,z) = (1,1,1), it is shown that
1 + ((1)^3 + 3 \times (1)^2 \times (1) \times {\partial z}/{\partial x}} - 2 \times (1) {\partial z}/{\partial x}} = 0
\therefore {\partial z}/{\partial x}} = -2.
// previous solution omitted x^2 in the first part of the implicit differentiation.
