d/(dt)(-3cos^2(t)sin(t))

Lösung

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

- 3 (- 2 cos (t) + 3 cos^{3} (t))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = cos^{2} (t), g = sin (t)

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

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

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

= - 3 ((- sin (2 t)) sin (t) + cos (t) cos^{2} (t))

Vereinfache

- 3 ((- sin (2 t)) sin (t) + cos (t) cos^{2} (t)) : - 3 (- 2 cos (t) + 3 cos^{3} (t))

= - 3 (- 2 cos (t) + 3 cos^{3} (t))

x \to 5 lim (x^{2})

x \to \infty lim ((x)!)

d er i v a t i v e π^{3}

\int_{1}^{\infty} \frac{4}{x ^{2} + 1} d x

\int 8 e^{8 x} sin (e^{8 x}) d x