Answer
w = xy + yz + xz, x = u + y, y = u - y, z = uy;
(u, y) = (1/2, 1)
$\frac{dw}{du}$=$\frac{dw}{dx}$.$\frac{dx}{du}$+$\frac{dw}{dy}$.$\frac{dy}{du}$+$\frac{dw}{dz}$.$\frac{dz}{du}$
$\frac{dw}{du}$=(y+z).1+(x+z).1+(y+x).(v)
$\frac{dw}{du}$=y+z+x+z+v(y+x)
=2z+x+y+v(y+x)
=2uv+u+v+u-v+v(u-v+u+v)
=2uv+2u+2uv
=2$\times$$\frac{1}{2}$+2$\times$$\frac{1}{2}$+2$\times$$\frac{1}{2}\times1$
=1+1+1
=3
$\frac{dw}{dv}$=$\frac{dw}{dx}$.$\frac{dx}{dv}$+$\frac{dw}{dy}$.$\frac{dy}{dv}$+$\frac{dw}{dz}$.$\frac{dz}{dv}$
$\frac{dw}{du}$=(y+z).1+(x+z)(-1)+(y+x).(u)
=y+z-x-z=(x+y)u
=u-v-u-v+(u+v+u-v).u
=-2v+2$u^{2}$
=-2+2$\times$$\frac{1}{2}^{2}$
=$\frac{-3}{2}$
