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Beliebt Rechnen >

derivative w(z)=6z^2e^z

Lösung

ableitung von

w (z) = 6 z^{2} e^{z}

Lösung

\frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

Schritte zur Lösung

w z = 6 z^{2} e^{z}

Behandle

z

wie

z (w)

Beide Seiten differenzieren:

z + w \frac{d z}{d w} = 6 (2 z \frac{d z}{d w} e^{z} + e^{z} \frac{d z}{d w} z^{2})

Isoliere

\frac{d z}{d w} : \frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

\frac{d z}{d w} = - \frac{z}{w - 12 e ^{z} z - 6 e ^{z} z ^{2}}

Graph

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