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Beliebt Rechnen >

derivative-10ln(xe^{x^8})

Lösung

ableitung von

- 10 ln (x e^{x^{8}})

Lösung

- 10 (\frac{1}{x} + 8 x^{7})

Schritte zur Lösung

\frac{d}{d x} (- 10 ln (x e^{x^{8}}))

Vereinfache

- 10 ln (x e^{x^{8}}) : - 10 (ln (x) + x^{8})

= \frac{d}{d x} (- 10 (ln (x) + x^{8}))

Entferne die Konstante:

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

= - 10 \frac{d}{d x} (ln (x) + x^{8})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - 10 (\frac{d}{d x} (ln (x)) + \frac{d}{d x} (x^{8}))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (x^{8}) = 8 x^{7}

= - 10 (\frac{1}{x} + 8 x^{7})

Graph

Beliebte Beispiele

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\int 6 y (x - y) d y

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