d/(dt)(sin(t)*cos(t))

Lösung

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

cos (2 t)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= cos (2 t)

x \frac{d ^{2} y}{d x ^{2}} + (2 \frac{d y}{d x}) = 0

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{3}}

\int_{1}^{2} x^{4} (ln (x))^{2} d x

\frac{d}{d x} (- \frac{1}{4 ( x + 1 ) ^{\frac{3}{2}}})

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