derivative of (x-6/(x^2-2x+12))

Lösung

\frac{d}{d x} (\frac{x - 6}{x ^{2} - 2 x + 12})

\frac{- x ^{2} + 12 x}{( x ^{2} - 2 x + 12 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 6}{x ^{2} - 2 x + 12})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 6 ) ( x ^{2} - 2 x + 12 ) - \frac{d}{d x} ( x ^{2} - 2 x + 12 ) ( x - 6 )}{( x ^{2} - 2 x + 12 ) ^{2}}

\frac{d}{d x} (x - 6) = 1

\frac{d}{d x} (x^{2} - 2 x + 12) = 2 x - 2

= \frac{1 \cdot ( x ^{2} - 2 x + 12 ) - ( 2 x - 2 ) ( x - 6 )}{( x ^{2} - 2 x + 12 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} - 2 x + 12 ) - ( 2 x - 2 ) ( x - 6 )}{( x ^{2} - 2 x + 12 ) ^{2}} : \frac{- x ^{2} + 12 x}{( x ^{2} - 2 x + 12 ) ^{2}}

= \frac{- x ^{2} + 12 x}{( x ^{2} - 2 x + 12 ) ^{2}}

x \to 0 lim (- 2 sin (x))

t an g e n t y = 3 x^{3} - 2 x, (1, 1)

x \to 0 lim (ln (- x))

x \to \infty lim (arctan (\frac{x + 1}{x + 2}))

\frac{d y}{d x} - 2 x y = 6 x