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

Lösung

ableitung von

\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}}

d er i v a t i v e y = (2 x + 1)^{3} + 6 x (2 x + 1)^{2}

\frac{\partial}{\partial y} (e^{- 3 x} cos (6 y))

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

\int x + 12 x^{2} d x

f (x) = (x - 2)^{2} (x - 3)^{3}