d/(dt)(4e^t*t)

Lösung

\frac{d}{d t} (4 e^{t} \cdot t)

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = e^{t}, g = t

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

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

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

= 4 (e^{t} t + 1 \cdot e^{t})

Vereinfache

= 4 (e^{t} t + e^{t})

\int_{2}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{d}{d x} (e^{\frac{x}{4}})

\int \frac{x ^{2} - 25}{2 x ^{2}} d x

\int x^{2} \cdot x^{3} + 3 d x

\frac{d y}{d x} = \frac{( 9 x ^{11} x ^{23} )}{y}