Question #8d476

1 Answer
Mar 2, 2016

f_x = ze^(xz)+y

f_y = x

Explanation:

When we differentiate with respect to a given variable, all other variables are treated as constants. Thus, given
f(x, y, z) = e^(xz)+xy

" "

f_x = d/dx(e^(xz)+xy)

=(d/dxe^(xz))+(d/dx(xy))

=ze^(xz)+y

and

f_y = d/dy(e^(xz)+xy)

=(d/dye^(xz))+(d/dyxy)

=x