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Beliebt Rechnen >

derivative of x(x^2+7^4)

Lösung

\frac{d}{d x} (x (x^{2} + 7)^{4})

Lösung

(x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

Schritte zur Lösung

\frac{d}{d x} (x (x^{2} + 7)^{4})

Wende die Produktregel an:

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

f = x, g = (x^{2} + 7)^{4}

= \frac{d x}{d x} (x^{2} + 7)^{4} + \frac{d}{d x} ((x^{2} + 7)^{4}) x

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

\frac{d}{d x} ((x^{2} + 7)^{4}) = 8 x (x^{2} + 7)^{3}

= 1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x

Vereinfache

1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x : (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

= (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

Graph

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