derivative of-cos(xsin(x))

Lösung

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

- cos (2 x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

Vereinfache

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

= - cos (2 x)

\int e^{2 x} cos (2 x) d x

\frac{d}{d x} (arctanh (sin (x)))

\int \frac{x}{( 3 x ^{2} - 4 ) ^{4}} d x

\int (4 x^{2} - 3 cos (x)) d x

\int sin (10 x) cos (5 x) d x