derivative of 6x^5ln(x+x^5)

Lösung

\frac{d}{d x} (6 x^{5} ln (x) + x^{5})

30 x^{4} ln (x) + 11 x^{4}

Schritte zur Lösung

\frac{d}{d x} (6 x^{5} ln (x) + x^{5})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (6 x^{5} ln (x)) + \frac{d}{d x} (x^{5})

\frac{d}{d x} (6 x^{5} ln (x)) = 6 (5 x^{4} ln (x) + x^{4})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 6 (5 x^{4} ln (x) + x^{4}) + 5 x^{4}

Vereinfache

6 (5 x^{4} ln (x) + x^{4}) + 5 x^{4} : 30 x^{4} ln (x) + 11 x^{4}

= 30 x^{4} ln (x) + 11 x^{4}

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