derivative x^2sin^3(3x)

Lösung

ableitung von

x^{2} sin^{3} (3 x)

2 x sin^{3} (3 x) + 9 sin^{2} (3 x) cos (3 x) x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = sin^{3} (3 x)

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

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

\frac{d}{d x} (sin^{3} (3 x)) = 9 sin^{2} (3 x) cos (3 x)

= 2 x sin^{3} (3 x) + 9 sin^{2} (3 x) cos (3 x) x^{2}

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