derivative of (x-3/(x^2+4))

Lösung

\frac{d}{d x} (\frac{x - 3}{x ^{2} + 4})

\frac{- x ^{2} + 6 x + 4}{( x ^{2} + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 3}{x ^{2} + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( x - 3 )}{( x ^{2} + 4 ) ^{2}}

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

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

= \frac{1 \cdot ( x ^{2} + 4 ) - 2 x ( x - 3 )}{( x ^{2} + 4 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} + 4 ) - 2 x ( x - 3 )}{( x ^{2} + 4 ) ^{2}} : \frac{- x ^{2} + 6 x + 4}{( x ^{2} + 4 ) ^{2}}

= \frac{- x ^{2} + 6 x + 4}{( x ^{2} + 4 ) ^{2}}

s l o p e (0.2) (6.6)

x \to 3 lim (\frac{x ^{2}}{9 - x ^{2}})

\frac{d}{d x} (\frac{( e ^{x} )}{x ^{2}})

t an g e n t \frac{2}{x - 1}

\int x^{- \frac{7}{3}} d x