d/(dt)(e^{2t}cos(4t))

Lösung

\frac{d}{d t} (e^{2 t} cos (4 t))

2 e^{2 t} cos (4 t) - 4 e^{2 t} sin (4 t)

Schritte zur Lösung

\frac{d}{d t} (e^{2 t} cos (4 t))

Wende die Produktregel an:

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

f = e^{2 t}, g = cos (4 t)

= \frac{d}{d t} (e^{2 t}) cos (4 t) + \frac{d}{d t} (cos (4 t)) e^{2 t}

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

\frac{d}{d t} (cos (4 t)) = - sin (4 t) \cdot 4

= e^{2 t} \cdot 2 cos (4 t) + (- sin (4 t) \cdot 4) e^{2 t}

Vereinfache

= 2 e^{2 t} cos (4 t) - 4 e^{2 t} sin (4 t)

d er i v a t i v e f (x) = (x^{4}) x^{2} + 2

\int \frac{48 x}{( x + 1 ) ^{2} ( 3 x + 1 )} d x

t^{2} y^{^{''}} - t (t + 2) y^{^{'}} + (t + 2) y = 0

t an g e n t y = 4 x^{2} + 3 x (- 3.27)

x \to 2 lim (\frac{( x + 2 )}{x - 2})