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Beliebt Rechnen >

derivative x^5e^x

Lösung

ableitung von

x^{5} e^{x}

Lösung

5 x^{4} e^{x} + e^{x} x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} e^{x})

Wende die Produktregel an:

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

f = x^{5}, g = e^{x}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} e^{x} + e^{x} x^{5}

Graph

Beliebte Beispiele

integral of 2*(x-6)^3

\int 2 \cdot (x - 6)^{3} d x

tangent f(x)=7+4x^2-2x^3,\at x=a

t an g e n t f (x) = 7 + 4 x^{2} - 2 x^{3}, at x = a

derivative 4e^{x^{-3}}

d er i v a t i v e 4 e^{x^{- 3}}

limit as x approaches 0 of 9x^2-4x+8

x \to 0 lim (9 x^{2} - 4 x + 8)

integral of sec^2(sqrt(x))

\int sec^{2} (x) d x