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Beliebt Rechnen >

derivative 6x(x^2+1)^2

Lösung

ableitung von

6 x (x^{2} + 1)^{2}

Lösung

6 (5 x^{4} + 6 x^{2} + 1)

Schritte zur Lösung

\frac{d}{d x} (6 x (x^{2} + 1)^{2})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x (x^{2} + 1)^{2})

Wende die Produktregel an:

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

f = x, g = (x^{2} + 1)^{2}

= 6 (\frac{d x}{d x} (x^{2} + 1)^{2} + \frac{d}{d x} ((x^{2} + 1)^{2}) x)

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= 6 (1 \cdot (x^{2} + 1)^{2} + 4 x (x^{2} + 1) x)

Vereinfache

6 (1 \cdot (x^{2} + 1)^{2} + 4 x (x^{2} + 1) x) : 6 (5 x^{4} + 6 x^{2} + 1)

= 6 (5 x^{4} + 6 x^{2} + 1)

Graph

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