derivative of sin(3xcos(x))

Lösung

\frac{d}{d x} (sin (3 x) cos (x))

3 cos (3 x) cos (x) - sin (x) sin (3 x)

Schritte zur Lösung

\frac{d}{d x} (sin (3 x) cos (x))

Wende die Produktregel an:

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

f = sin (3 x), g = cos (x)

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

= cos (3 x) \cdot 3 cos (x) + (- sin (x)) sin (3 x)

Vereinfache

= 3 cos (3 x) cos (x) - sin (x) sin (3 x)