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Beliebt Rechnen >

derivative of f(x^2(x))

Lösung

\frac{d}{d x} (f (x) (x)^{2} (x))

Lösung

3 x^{2} f (x) + \frac{d}{d x} (f (x)) x^{3}

Schritte zur Lösung

\frac{d}{d x} (f (x) (x)^{2} (x))

Vereinfache

f (x) (x)^{2} (x) : x^{3} f (x)

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

Wende die Produktregel an:

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

f = x^{3}, g = f (x)

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 3 x^{2} f (x) + \frac{d}{d x} (f (x)) x^{3}

Beliebte Beispiele

\frac{d}{d t} (t^{3} e^{t})

derivative of arccos(7x)

\frac{d}{d x} (arccos (7 x))

derivative of sinh(3x^2+1)

\frac{d}{d x} (sinh (3 x^{2} + 1))

a re a x^{4}, 8 x

(cos (\frac{π}{x}))^{^{'}}