derivative (x^2-4x+2)/(x+3)

Lösung

ableitung von

\frac{x ^{2} - 4 x + 2}{x + 3}

\frac{x ^{2} + 6 x - 14}{( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 4 x + 2}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 4 x + 2 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x ^{2} - 4 x + 2 )}{( x + 3 ) ^{2}}

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

\frac{d}{d x} (x + 3) = 1

= \frac{( 2 x - 4 ) ( x + 3 ) - 1 \cdot ( x ^{2} - 4 x + 2 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{( 2 x - 4 ) ( x + 3 ) - 1 \cdot ( x ^{2} - 4 x + 2 )}{( x + 3 ) ^{2}} : \frac{x ^{2} + 6 x - 14}{( x + 3 ) ^{2}}

= \frac{x ^{2} + 6 x - 14}{( x + 3 ) ^{2}}

x \to 1 lim (x^{2} - 1)

\int 3 x^{2} - 5 d x

in v erse l a pl a ce \frac{e ^{1 - s}}{s ^{2} - 1}

t a y l or \frac{e ^{x^{2}} - 1}{x ^{2}}

\frac{d}{d x} (\frac{x ^{\frac{1}{3}} + x}{ln ( x ) + x})