d/(dt)(3te^t)

Lösung

\frac{d}{d t} (3 t e^{t})

3 (e^{t} + e^{t} t)

Schritte zur Lösung

\frac{d}{d t} (3 t e^{t})

Entferne die Konstante:

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

= 3 \frac{d}{d t} (t e^{t})

Wende die Produktregel an:

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

f = t, g = e^{t}

= 3 (\frac{d t}{d t} e^{t} + \frac{d}{d t} (e^{t}) t)

\frac{d t}{d t} = 1

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

= 3 (1 \cdot e^{t} + e^{t} t)

Vereinfache

= 3 (e^{t} + e^{t} t)

\int_{- 3}^{- 1} (x + 2)^{99} d x

d er i v a t i v e 7 x - \frac{9}{x ^{6}}

t an g e n t f (x) = x e^{- \frac{x}{2}}, at x = \frac{1}{2}

t^{2} y^{^{''}} + 2 t y^{^{'}} - 30 y = 0

x \to 3 lim (\frac{( x + 3 )}{x - 3})