Answer
$\dfrac{(-v^2w du+dv-uv^2dw)}{(1+uvw)^2}$
Work Step by Step
The differential form for the given function can be calculated as:
$dT=\dfrac{\partial T}{\partial u} du +\dfrac{\partial T}{\partial v} dv+ \dfrac{\partial T}{\partial w} dw$
$dT=\dfrac{-v \times (vw)}{(1+uvw)^2}du+\dfrac{1+uvw-v \times (uw)}{(1+uvw)^2} dv+\dfrac{-v \times (uv)}{(1+uvw)^2} dw$
This implies that
$dT=\dfrac{(-v^2w du+dv-uv^2dw)}{(1+uvw)^2}$
