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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

\int (\frac{5}{x} - \frac{3}{x ^{2}}) d x

\int_{5}^{8} \frac{6}{x - 5} d x

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\frac{\partial}{\partial x} (ln (x - y^{2}))

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