derivative of (x-1/(x^2+4))

Lösung

\frac{d}{d x} (\frac{x - 1}{x ^{2} + 4})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 1}{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 - 1 ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( x - 1 )}{( x ^{2} + 4 ) ^{2}}

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

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

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

Vereinfache

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

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

x^{2} \frac{d y}{d x} = x y + 3 y^{2}

d er i v a t i v e 50 x^{2} e^{- x} + 8

\frac{d}{d u} (\frac{u}{v})

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

x \to 0 lim (3 x + 1)