Answer
$f_x=-1/2(x^2+y^2+z^2)^{-3/2}\times 2x$
$f_y=-1/2(x^2+y^2+z^2)^{-3/2}\times 2y$
$f_z=-1/2(x^2+y^2+z^2)^{-3/2}\times 2z$
Work Step by Step
Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y and z as constants, with respect to y, treat x and z as constants, and with respect to z, treat x and y as constants:
$f_x=-1/2(x^2+y^2+z^2)^{-3/2}\times 2x$
$f_y=-1/2(x^2+y^2+z^2)^{-3/2}\times 2y$
$f_z=-1/2(x^2+y^2+z^2)^{-3/2}\times 2z$
