(\partial)/(\partial x)((e^v)/(u(v,x)+v^9))

Lösung

\frac{\partial}{\partial x} (\frac{e ^{v}}{u ( v , x ) + v ^{9}})

e^{v} (- \frac{1}{( u ( v , x ) + v ^{9} ) ^{2}} (\frac{\partial}{\partial x} (u (v, x)) + 0))

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{e ^{v}}{u ( v , x ) + v ^{9}})

Behandle

v

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{v} \frac{\partial}{\partial x} (\frac{1}{u ( v , x ) + v ^{9}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= e^{v} \frac{\partial}{\partial x} ((u (v, x) + v^{9})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( u ( v , x ) + v ^{9} ) ^{2}} \frac{\partial}{\partial x} (u (v, x) + v^{9})

= - \frac{1}{( u ( v , x ) + v ^{9} ) ^{2}} \frac{\partial}{\partial x} (u (v, x) + v^{9})

\frac{\partial}{\partial x} (u (v, x) + v^{9}) = \frac{\partial}{\partial x} (u (v, x)) + 0

= e^{v} (- \frac{1}{( u ( v , x ) + v ^{9} ) ^{2}} (\frac{\partial}{\partial x} (u (v, x)) + 0))

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