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Beliebt Rechnen >

derivative of e^{-x}x^2

Lösung

\frac{d}{d x} (e^{- x} x^{2})

Lösung

- e^{- x} x^{2} + 2 e^{- x} x

Schritte zur Lösung

\frac{d}{d x} (e^{- x} x^{2})

Wende die Produktregel an:

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

f = e^{- x}, g = x^{2}

= \frac{d}{d x} (e^{- x}) x^{2} + \frac{d}{d x} (x^{2}) e^{- x}

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

\frac{d}{d x} (x^{2}) = 2 x

= (- e^{- x}) x^{2} + 2 x e^{- x}

Vereinfache

= - e^{- x} x^{2} + 2 e^{- x} x

Graph

Beliebte Beispiele

limit as x approaches-2-of (x+5)/(x+4)

x \to - 2 - lim (\frac{x + 5}{x + 4})

derivative of (x^2-9^{2/3})

\frac{d}{d x} ((x^{2} - 9)^{\frac{2}{3}})

integral of (3x^2+2x-3)

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

sum from n=1 to infinity of 9/((n+1)!)

n = 1 \sum \infty \frac{9}{( n + 1 ) !}

tangent f(x)=8x^2,\at x=10

t an g e n t f (x) = 8 x^{2}, at x = 10