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Beliebt Rechnen >

d/(dt)(5e^tcos(t))

Lösung

\frac{d}{d t} (5 e^{t} cos (t))

Lösung

5 (e^{t} cos (t) - e^{t} sin (t))

Schritte zur Lösung

\frac{d}{d t} (5 e^{t} cos (t))

Entferne die Konstante:

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

= 5 \frac{d}{d t} (e^{t} cos (t))

Wende die Produktregel an:

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

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

= 5 (\frac{d}{d t} (e^{t}) cos (t) + \frac{d}{d t} (cos (t)) e^{t})

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

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

= 5 (e^{t} cos (t) + (- sin (t)) e^{t})

Vereinfache

= 5 (e^{t} cos (t) - e^{t} sin (t))

Graph

Beliebte Beispiele

derivative f(x)=cos(5x)

d er i v a t i v e f (x) = cos (5 x)

12x^3-3ysqrt(x^4+1)y^'=0

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integral of (e^u)/u

\int \frac{e ^{u}}{u} d u

derivative (x^2+4)^3

d er i v a t i v e (x^{2} + 4)^{3}

integral of (θ^6+sec^2(θ))

\int (θ^{6} + sec^{2} (θ)) d θ