Answer
$f_x=\dfrac{yz}{\sqrt {(1-x^2y^2z^2)}}$ ;
$f_y=\dfrac{xz}{\sqrt {(1-x^2y^2z^2)}}$ ;
$f_z=\dfrac{xy}{\sqrt {(1-x^2y^2z^2)}}$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ and $z$ as a constant, and vice versa:
$f_x=\dfrac{1}{\sqrt {(1-(xyz)^2)}}\times yz=\dfrac{yz}{\sqrt {(1-x^2y^2z^2)}} ;\\f_y=\dfrac{1}{\sqrt {(1-(xyz)^2)}}\times xz=\dfrac{xz}{\sqrt {(1-x^2y^2z^2)}} ;f_z=\dfrac{1}{\sqrt {(1-(xyz)^2)}}\times xy=\dfrac{xy}{\sqrt {(1-x^2y^2z^2)}}$
