derivative of ((2x-1)/(x^2))

Lösung

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

\frac{2 ( - x + 1 )}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ^{2} - 2 x ( 2 x - 1 )}{( x ^{2} ) ^{2}} : \frac{2 ( - x + 1 )}{x ^{3}}

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

in v erse l a pl a ce \frac{1}{( s - 2 )}

\frac{d}{d x} (\frac{x}{x + 4})

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

\int \frac{3}{x + 3 + x} d x

\int x + \frac{1}{x} - 7 d x