derivative of xe^{(-(x^2/8)})

Lösung

\frac{d}{d x} (x e^{(- \frac{x ^{2}}{8})})

e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

Schritte zur Lösung

\frac{d}{d x} (x e^{(- \frac{x ^{2}}{8})})

Wende die Produktregel an:

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

f = x, g = e^{- \frac{x ^{2}}{8}}

= \frac{d x}{d x} e^{- \frac{x ^{2}}{8}} + \frac{d}{d x} (e^{- \frac{x ^{2}}{8}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- \frac{x ^{2}}{8}}) = - \frac{e ^{- \frac{x ^{2}}{8}} x}{4}

= 1 \cdot e^{- \frac{x ^{2}}{8}} + (- \frac{e ^{- \frac{x ^{2}}{8}} x}{4}) x

Vereinfache

1 \cdot e^{- \frac{x ^{2}}{8}} + (- \frac{e ^{- \frac{x ^{2}}{8}} x}{4}) x : e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

= e^{- \frac{x ^{2}}{8}} - \frac{e ^{- \frac{x ^{2}}{8}} x ^{2}}{4}

d er i v a t i v e f (x) = - \frac{1}{6} (x^{- 6} - x^{12})

x y^{^{'}} + y = x^{\frac{3}{2}} y^{\frac{5}{2}} ln (x)

t an g e n t e^{6 x}

d er i v a t i v e \frac{x + 9}{x}

\frac{d}{d t} (e^{- t} sin (2 t))