derivative (x-4)/(x+2)

Lösung

ableitung von

\frac{x - 4}{x + 2}

\frac{6}{( x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 4}{x + 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 4 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x - 4 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x - 4) = 1

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

= \frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 4 )}{( x + 2 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x + 2 ) - 1 \cdot ( x - 4 )}{( x + 2 ) ^{2}} : \frac{6}{( x + 2 ) ^{2}}

= \frac{6}{( x + 2 ) ^{2}}

\int \frac{2 x + 1}{( x - 1 ) ( x + 4 ) ^{2}} d x

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

\int \frac{- 2 y}{x} d x

x \to 5 + lim (\frac{- 3}{x ^{2} - 25})

(1 + x^{2}) y^{^{'}} = x (1 - y)