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Beliebt Rechnen >

derivative t^3e^tt

Lösung

ableitung von

t^{3} e^{t} t

Lösung

e^{t} t^{4} + 4 t^{3} e^{t}

Schritte zur Lösung

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

Vereinfache

t^{3} e^{t} t : e^{t} t^{4}

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

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

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

\frac{d}{d t} (t^{4}) = 4 t^{3}

= e^{t} t^{4} + 4 t^{3} e^{t}

Graph

Beliebte Beispiele

limit as n approaches infinity of c^n

n \to \infty lim (c^{n})

y^{''}+y^'-2y=0,y(0)=1,y^'(0)=1

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 1

(3 cos (t))^{^{'}}

derivative of x^3-9x+3

\frac{d}{d x} (x^{3} - 9 x + 3)

fläche f(x)= 1/(x+2),[3,6]

a re a f (x) = \frac{1}{x + 2}, [3, 6]