derivative of x^{-2}e^{2x}

Lösung

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

- \frac{2 e ^{2 x}}{x ^{3}} + \frac{2 e ^{2 x}}{x ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} (\frac{x}{tan ( x )})

in v erse l a pl a ce \frac{2 e ^{- 2 s}}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to a lim (2 f (x) - 3 g (x))

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