derivative cos(3t)sin(2t)

Lösung

ableitung von

cos (3 t) sin (2 t)

- 3 sin (3 t) sin (2 t) + 2 cos (2 t) cos (3 t)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

= - 3 sin (3 t) sin (2 t) + 2 cos (2 t) cos (3 t)

\int \frac{6}{sin ^{2} ( x )} d x

d er i v a t i v e f (x) = \frac{x ^{3}}{3} + x^{2} + 4 x - 10

t an g e n t y = 10 x - x^{2}, (5, 26)

\int \frac{1}{x - ln ^{2} ( x ) + ln ( x ) + 3} d x

\int \frac{2 x + 5}{9 - x ^{2}} d x