(\partial ^2)/(\partial {u)(w)\partial w}(e^{{u}(w)-w})

解

\frac{\partial ^{3}}{\partial u ( w ) \partial w ^{2}} (e^{u (w) - w})

解答ステップ

\frac{\partial ^{3}}{\partial u ( w ) \partial w ^{2}} (e^{u (w) - w})

\frac{\partial}{\partial u ( w )} (e^{u (w) - w}) = e^{u (w) - w}

= \frac{\partial ^{2}}{\partial w ^{2}} (e^{u (w) - w})

\frac{\partial}{\partial w} (e^{u (w) - w}) = e^{u (w) - w} (\frac{\partial}{\partial w} (u (w)) - 1)

= \frac{\partial}{\partial w} (e^{u (w) - w} (\frac{\partial}{\partial w} (u (w)) - 1))

\frac{\partial}{\partial w} (e^{u (w) - w} (\frac{\partial}{\partial w} (u (w)) - 1)) = e^{u (w) - w} (\frac{\partial}{\partial w} (u (w)) - 1)^{2} + e^{u (w) - w} \frac{\partial ^{2}}{\partial w ^{2}} (u (w))

= e^{u (w) - w} (\frac{\partial}{\partial w} (u (w)) - 1)^{2} + e^{u (w) - w} \frac{\partial ^{2}}{\partial w ^{2}} (u (w))