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Beliebt Rechnen >

(\partial}{\partial x}(200e^{-x^2-\frac{y^2)/4-(z^2)/9})

Lösung

\frac{\partial}{\partial x} (200 e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}})

Lösung

- 400 e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}} x

Schritte zur Lösung

\frac{\partial}{\partial x} (200 e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}})

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

= 200 \frac{\partial}{\partial x} (e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}})

Wende die Kettenregel an:

e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}} \frac{\partial}{\partial x} (- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9})

= e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}} \frac{\partial}{\partial x} (- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9})

\frac{\partial}{\partial x} (- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}) = - 2 x

= 200 e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}} (- 2 x)

Vereinfache

= - 400 e^{- x^{2} - \frac{y ^{2}}{4} - \frac{z ^{2}}{9}} x

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