(\partial ^2)/(\partial {u)(v)\partial v}(8ve^{-6{u}(v)})

解

\frac{\partial ^{3}}{\partial u ( v ) \partial v ^{2}} (8 v e^{- 6 u (v)})

解答ステップ

\frac{\partial ^{3}}{\partial u ( v ) \partial v ^{2}} (8 v e^{- 6 u (v)})

\frac{\partial}{\partial u ( v )} (8 v e^{- 6 u (v)}) = - 48 e^{- 6 u (v)} v

= \frac{\partial ^{2}}{\partial v ^{2}} (- 48 e^{- 6 u (v)} v)

\frac{\partial}{\partial v} (- 48 e^{- 6 u (v)} v) = - 48 (- 6 e^{- 6 u (v)} v \frac{\partial}{\partial v} (u (v)) + e^{- 6 u (v)})

= \frac{\partial}{\partial v} (- 48 (- 6 e^{- 6 u (v)} v \frac{\partial}{\partial v} (u (v)) + e^{- 6 u (v)}))

\frac{\partial}{\partial v} (- 48 (- 6 e^{- 6 u (v)} v \frac{\partial}{\partial v} (u (v)) + e^{- 6 u (v)})) = - 48 (36 e^{- 6 u (v)} v \frac{\partial}{\partial v} (u (v))^{2} - 6 e^{- 6 u (v)} v \frac{\partial ^{2}}{\partial v ^{2}} (u (v)) - 12 e^{- 6 u (v)} \frac{\partial}{\partial v} (u (v)))

= - 48 (36 e^{- 6 u (v)} v \frac{\partial}{\partial v} (u (v))^{2} - 6 e^{- 6 u (v)} v \frac{\partial ^{2}}{\partial v ^{2}} (u (v)) - 12 e^{- 6 u (v)} \frac{\partial}{\partial v} (u (v)))