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Beliebt Rechnen >

derivative y=x^5sin^2(2x)

Lösung

ableitung von

y = x^{5} sin^{2} (2 x)

Lösung

5 x^{4} sin^{2} (2 x) + 2 sin (4 x) x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} sin^{2} (2 x))

Wende die Produktregel an:

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

f = x^{5}, g = sin^{2} (2 x)

= \frac{d}{d x} (x^{5}) sin^{2} (2 x) + \frac{d}{d x} (sin^{2} (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} sin^{2} (2 x) + 2 sin (4 x) x^{5}

Graph

Beliebte Beispiele

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\int_{- 2}^{2} \frac{1}{4 + x ^{2}} d x

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