derivative sin(2x)cos(3x)

Lösung

ableitung von

sin (2 x) cos (3 x)

2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = sin (2 x), g = cos (3 x)

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

= cos (2 x) \cdot 2 cos (3 x) + (- sin (3 x) \cdot 3) sin (2 x)

Vereinfache

= 2 cos (2 x) cos (3 x) - 3 sin (3 x) sin (2 x)

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

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

\int_{- 1}^{2} (3 x^{2} - 2 x + 3) d x

n = 0 \sum \infty 1 - (0.2)^{n}

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