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Beliebt Rechnen >

derivative of {f}(x(x)^3(x))

Lösung

\frac{d}{d x} (f (x) (x)^{3} (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (f (x) (x)^{3} (x))

Vereinfache

f (x) (x)^{3} (x) : x^{4} f (x)

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

Wende die Produktregel an:

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

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

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

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

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

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