d/(dt)(e^t(cos(t)))

Lösung

\frac{d}{d t} (e^{t} (cos (t)))

e^{t} cos (t) - e^{t} sin (t)

Schritte zur Lösung

\frac{d}{d t} (e^{t} (cos (t)))

Wende die Produktregel an:

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

f = e^{t}, g = cos (t)

= \frac{d}{d t} (e^{t}) cos (t) + \frac{d}{d t} (cos (t)) e^{t}

\frac{d}{d t} (e^{t}) = e^{t}

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

= e^{t} cos (t) + (- sin (t)) e^{t}

Vereinfache

= e^{t} cos (t) - e^{t} sin (t)

\int_{0}^{\frac{3}{4}} \frac{1}{9 + 16 x ^{2}} d x

\frac{d}{d x} (\frac{1}{2 π} e^{- \frac{x ^{2}}{2}})

\frac{d}{d x} (A x^{2} e^{x} + B x e^{x} + C e^{x})

\int \frac{1}{10 x} d x

d er i v a t i v e y^{2}