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Beliebt Rechnen >

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

Lösung

ableitung von

3 x (x^{4} + 5)^{5}

Lösung

3 ((x^{4} + 5)^{5} + 20 x^{4} (x^{4} + 5)^{4})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = (x^{4} + 5)^{5}

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot (x^{4} + 5)^{5} + 20 x^{3} (x^{4} + 5)^{4} x)

Vereinfache

3 (1 \cdot (x^{4} + 5)^{5} + 20 x^{3} (x^{4} + 5)^{4} x) : 3 ((x^{4} + 5)^{5} + 20 x^{4} (x^{4} + 5)^{4})

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

Graph

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