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

Lösung

ableitung von

\frac{x}{x ^{2} - x + 1}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

t a y l or \frac{1}{x - 1}, 25

d er i v a t i v e f (x) = x - 8 3 x

\int_{1}^{5} \frac{x}{5 - x} d x

l a pl a ce t r an s f or m \frac{9}{4} t^{2} e^{2 t} e^{3 t}

\frac{d}{d x} (x tan (2 x) + 7)