derivative of (3x^2-18x+25/(x^2-6x+8))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 18 x + 25}{x ^{2} - 6 x + 8})

\frac{- 2 x + 6}{( x ^{2} - 6 x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 18 x + 25}{x ^{2} - 6 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{2} - 18 x + 25 ) ( x ^{2} - 6 x + 8 ) - \frac{d}{d x} ( x ^{2} - 6 x + 8 ) ( 3 x ^{2} - 18 x + 25 )}{( x ^{2} - 6 x + 8 ) ^{2}}

\frac{d}{d x} (3 x^{2} - 18 x + 25) = 6 x - 18

\frac{d}{d x} (x^{2} - 6 x + 8) = 2 x - 6

= \frac{( 6 x - 18 ) ( x ^{2} - 6 x + 8 ) - ( 2 x - 6 ) ( 3 x ^{2} - 18 x + 25 )}{( x ^{2} - 6 x + 8 ) ^{2}}

Multipliziere aus

(6 x - 18) (x^{2} - 6 x + 8) - (2 x - 6) (3 x^{2} - 18 x + 25) : - 2 x + 6

= \frac{- 2 x + 6}{( x ^{2} - 6 x + 8 ) ^{2}}

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

in v erse l a pl a ce \frac{1 - e ^{- 2 s}}{6 s ^{2}}

x \to 0 lim (- cos (x) + 1)

y = x (1 - x)^{6}

in v erse l a pl a ce f (s) = s - 3 (s^{2} + 4 s + 13)