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Beliebt Rechnen >

derivative of 3(5x^4+5x^3^4)

Lösung

\frac{d}{d x} (3 (5 x^{4} + 5 x^{3})^{4})

Lösung

12 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

Schritte zur Lösung

\frac{d}{d x} (3 (5 x^{4} + 5 x^{3})^{4})

Entferne die Konstante:

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

= 3 \frac{d}{d x} ((5 x^{4} + 5 x^{3})^{4})

Wende die Kettenregel an:

4 (5 x^{4} + 5 x^{3})^{3} \frac{d}{d x} (5 x^{4} + 5 x^{3})

= 4 (5 x^{4} + 5 x^{3})^{3} \frac{d}{d x} (5 x^{4} + 5 x^{3})

\frac{d}{d x} (5 x^{4} + 5 x^{3}) = 20 x^{3} + 15 x^{2}

= 3 \cdot 4 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

Vereinfache

= 12 (5 x^{4} + 5 x^{3})^{3} (20 x^{3} + 15 x^{2})

Graph

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