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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} (arcsin (\frac{a x}{4}))

\frac{\partial}{\partial y} (- 5 e^{x} cos (yz))

\int \frac{a}{2} x + \frac{a}{2} d x

x \to 8 lim (2 x - 7 x^{2})