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

Lösung

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

- 2 (cos^{2} (t) (cos (t) csc (2 t) - 2 cot (2 t) csc (2 t) sin (t)) - sin (t))

Schritte zur Lösung

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

Vereinfache

- \frac{2 cos ^{2} ( t ) sin ( t )}{sin ( 2 t )} : - 2 cos^{2} (t) sin (t) csc (2 t)

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= - 2 (cos^{2} (t) (cos (t) csc (2 t) - 2 cot (2 t) csc (2 t) sin (t)) - sin (t))

\int \frac{1}{x ( y ) ^{2} + 1} d x

x \to 3 lim (6 2 - x)

\int_{2}^{5} x^{2} ln (3 x) d x

x \frac{d y}{d x} + y = sec (x y)

\frac{d}{d x} (2 x e^{x + 3} + e^{x + 3} x^{2})