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Beliebt Rechnen >

d/(dt)(te^{at})

Lösung

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

Lösung

e^{a t} + a e^{a t} t

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = t, g = e^{a t}

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

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

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

= 1 \cdot e^{a t} + e^{a t} a t

Vereinfache

= e^{a t} + a e^{a t} t

Graph

Beliebte Beispiele

(\partial)/(\partial y)(x^2y^3+2x^4y)

\frac{\partial}{\partial y} (x^{2} y^{3} + 2 x^{4} y)

derivative of sqrt(7-10x)

\frac{d}{d x} (7 - 10 x)

integral of (sin(x))/(5+cos^2(x))

\int \frac{sin ( x )}{5 + cos ^{2} ( x )} d x

derivative of 1-|1-x|

\frac{d}{d x} (1 - ∣ 1 - x ∣)

integral of (x^4)/x

\int \frac{x ^{4}}{x} d x