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Beliebt Rechnen >

derivative of 9sin(xcos(x))

Lösung

\frac{d}{d x} (9 sin (x) cos (x))

Lösung

9 cos (2 x)

Schritte zur Lösung

\frac{d}{d x} (9 sin (x) cos (x))

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = sin (x), g = cos (x)

= 9 (\frac{d}{d x} (sin (x)) cos (x) + \frac{d}{d x} (cos (x)) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (cos (x)) = - sin (x)

= 9 (cos (x) cos (x) + (- sin (x)) sin (x))

Vereinfache

9 (cos (x) cos (x) + (- sin (x)) sin (x)) : 9 cos (2 x)

= 9 cos (2 x)

Graph

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