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Beliebt Rechnen >

derivative t^{11}ln|t|

Lösung

ableitung von

t^{11} ln ∣ t ∣

Lösung

11 t^{10} ln ∣ t ∣ + t^{10}

Schritte zur Lösung

\frac{d}{d t} (t^{11} ln ∣ t ∣)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{11}, g = ln ∣ t ∣

= \frac{d}{d t} (t^{11}) ln ∣ t ∣ + \frac{d}{d t} (ln ∣ t ∣) t^{11}

\frac{d}{d t} (t^{11}) = 11 t^{10}

\frac{d}{d t} (ln ∣ t ∣) = \frac{1}{t}

= 11 t^{10} ln ∣ t ∣ + \frac{1}{t} t^{11}

\frac{1}{t} t^{11} = t^{10}

= 11 t^{10} ln ∣ t ∣ + t^{10}

Graph

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