derivative of (x-1/(x^2-3x+3))

Lösung

\frac{d}{d x} (\frac{x - 1}{x ^{2} - 3 x + 3})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 1}{x ^{2} - 3 x + 3})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1}{( 100 + x ^{2} ) ^{2}} d x

d er i v a t i v e f (x) = 6 x^{5}

d er i v a t i v e sin (x) ln (cos (x))

x \to - 1 lim (3 x^{2} + \frac{4}{x ^{2}})

\int - 9 cot (x) ln (sin (x)) d x