derivative of (x-4/(x^2-2x+8))

Lösung

\frac{d}{d x} (\frac{x - 4}{x ^{2} - 2 x + 8})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 4}{x ^{2} - 2 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 4 ) ( x ^{2} - 2 x + 8 ) - \frac{d}{d x} ( x ^{2} - 2 x + 8 ) ( x - 4 )}{( x ^{2} - 2 x + 8 ) ^{2}}

\frac{d}{d x} (x - 4) = 1

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

= \frac{1 \cdot ( x ^{2} - 2 x + 8 ) - ( 2 x - 2 ) ( x - 4 )}{( x ^{2} - 2 x + 8 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} - 2 x + 8 ) - ( 2 x - 2 ) ( x - 4 )}{( x ^{2} - 2 x + 8 ) ^{2}} : \frac{- x ^{2} + 8 x}{( x ^{2} - 2 x + 8 ) ^{2}}

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

\frac{\partial}{\partial x} ((x^{2} - y^{2}) ln (x y))

\frac{d}{d x} (9 sin^{2} (x))

a re a y = x^{2} - 14, y = 13 x

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

in v erse l a pl a ce \frac{10}{( s ( s + 1 ) )}