derivative of ((e^x)/(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

t an g e n t \frac{2}{x - 1}

\int x^{- \frac{7}{3}} d x

\frac{d}{d x} (625 sin (5 x))

\int \frac{32 x ^{2}}{( x - 6 ) ( x + 2 ) ^{2}} d x

\int x^{3} x^{2} + 26 d x