# use implicit differentiation to find $\partial z/\partial x$, $\partial z/\partial y$

I can't find the word implicit differentiation anywhere in the book, but I'm assuming it means solve for $z$ in this case and differentiate with respect to $x$, then $y$ in this problem. But when I took the derivative with respect to $x$ of 47 after solving for $z$, i get a different answer.

I got $$z = \dfrac{\sqrt{-x^2-2y^2+1}}{\sqrt{3}}$$

and for the derivative of that:

$$-\dfrac{x}{\sqrt{3}\sqrt{-x^2-2y^2+1}}$$

(i got these results on https://www.derivative-calculator.net/)

this is different than the answer in the book. am i not supposed to solve for $z$ and differentiate with respect to $x$ then $y$? Is this another form of the answer? help..

the answer is $-x/3z$ ... which I don't get..