Answer
$f_x=\frac{1}{x+2y+3z}$
$f_y=\frac{2}{x+2y+3z}$
$f_z=\frac{3}{x+2y+3z}$
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:
$f_x=\frac{1}{x+2y+3z}\times 1$
$f_y=\frac{1}{x+2y+3z}\times 2=\frac{2}{x+2y+3z}$
$f_z=\frac{1}{x+2y+3z}\times3=\frac{3}{x+2y+3z}$
