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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{x y z}{x ^{2} + y ^{2} + z ^{2}})

x \to 5 lim (- x^{2} + 5 x - 8)

\int \frac{cos ^{2} ( x ) sin ( 2 x )}{2} d x

\int (y sin (x)) d x

s l o p e (- 3, - 8), (4, 6)