derivative of x*e^{-1/(x^2})

Lösung

\frac{d}{d x} (x \cdot e^{- \frac{1}{x ^{2}}})

e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x e^{- \frac{1}{x ^{2}}})

Wende die Produktregel an:

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

f = x, g = e^{- \frac{1}{x ^{2}}}

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

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

\frac{d}{d x} (e^{- \frac{1}{x ^{2}}}) = \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}}

= 1 \cdot e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}} x

Vereinfache

1 \cdot e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}} x : e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{2}}

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

(e^{- 5 x})^{^{'}}

\int \frac{x + 4}{x} d x

\frac{d}{d x} (a x^{3} ln (\frac{x}{4}) + b x^{2} (x - 4))

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

\frac{d y}{d t} = \frac{( y + 3 )}{( 1 - y )}