Answer
At $\left( {T,v} \right) = \left( { - 10,15} \right)$:
$\frac{{\partial W}}{{\partial v}}{|_{\left( {T,v} \right) = \left( { - 10,15} \right)}} \simeq - 0.31$
$\Delta W \simeq - 0.62$
Work Step by Step
We have
$W = 13.1267 + 0.6215T - 13.947{v^{0.16}} + 0.486T{v^{0.16}}$
So,
$\frac{{\partial W}}{{\partial v}} = - 0.16 \times 13.947{v^{ - 0.84}} + 0.16 \times 0.486T{v^{ - 0.84}}$
$\frac{{\partial W}}{{\partial v}} = - 2.23152{v^{ - 0.84}} + 0.07776T{v^{ - 0.84}}$
$\frac{{\partial W}}{{\partial v}}{|_{\left( {T,v} \right) = \left( { - 10,15} \right)}} \simeq - 0.31$
Next, we estimate the change of wind-chill temperature $W$ if $\Delta v = 2$ at $\left( {T,v} \right) = \left( { - 10,15} \right)$:
$\Delta W = \frac{{\partial W}}{{\partial v}}{|_{\left( {T,v} \right) = \left( { - 10,15} \right)}}\Delta v$
$\Delta W \simeq - 0.31 \times 2 \simeq - 0.62$
