derivative of x^2e^{(-x/(10)})

Lösung

\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

- \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

Schritte zur Lösung

\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

Vereinfache

x^{2} e^{\frac{- x}{10}} : e^{- \frac{x}{10}} x^{2}

= \frac{d}{d x} (e^{- \frac{x}{10}} x^{2})

Wende die Produktregel an:

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

f = e^{- \frac{x}{10}}, g = x^{2}

= \frac{d}{d x} (e^{- \frac{x}{10}}) x^{2} + \frac{d}{d x} (x^{2}) e^{- \frac{x}{10}}

\frac{d}{d x} (e^{- \frac{x}{10}}) = - \frac{1}{10} e^{- \frac{x}{10}}

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

= (- \frac{1}{10} e^{- \frac{x}{10}}) x^{2} + 2 x e^{- \frac{x}{10}}

Vereinfache

(- \frac{1}{10} e^{- \frac{x}{10}}) x^{2} + 2 x e^{- \frac{x}{10}} : - \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

= - \frac{e ^{- \frac{x}{10}} x ^{2}}{10} + 2 e^{- \frac{x}{10}} x

t an g e n t f (x) = \frac{x}{x ^{2} - 15}, at x = 4

y^{^{''}} + 25 y^{^{'}} = 0

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\int (10 x + 4) 5 x^{2} + 4 x d x

x \to 1 lim (1 - x)