derivative e^tsin(2t)

Lösung

ableitung von

e^{t} sin (2 t)

e^{t} sin (2 t) + cos (2 t) \cdot 2 e^{t}

Schritte zur Lösung

\frac{d}{d t} (e^{t} sin (2 t))

Wende die Produktregel an:

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

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

= \frac{d}{d t} (e^{t}) sin (2 t) + \frac{d}{d t} (sin (2 t)) e^{t}

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

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

= e^{t} sin (2 t) + cos (2 t) \cdot 2 e^{t}

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

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

\int_{0}^{\infty} x^{- 3} d x

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 40 y = 1 - 4 t

\int - \frac{1}{2} cos (2 x) d x