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Beliebt Rechnen >

derivative sin^3(xco)s^5x

Lösung

ableitung von

sin^{3} (x co) s^{5} x

Lösung

s^{5} (3 c x o sin^{2} (c x o) cos (c x o) + sin^{3} (c x o))

Schritte zur Lösung

\frac{d}{d x} (sin^{3} (x co) s^{5} x)

Behandle

c, o, s

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= s^{5} \frac{d}{d x} (sin^{3} (x co) x)

Wende die Produktregel an:

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

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

= s^{5} (\frac{d}{d x} (sin^{3} (x co)) x + \frac{d x}{d x} sin^{3} (x co))

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

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

= s^{5} (3 co sin^{2} (co x) cos (co x) x + 1 \cdot sin^{3} (x co))

Vereinfache

= s^{5} (3 c x o sin^{2} (c x o) cos (c x o) + sin^{3} (c x o))

Graph

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