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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

n = 1 \sum \infty \frac{( n + 6 )}{2}

a re a 2 x, \frac{x}{2}

x \to 0 lim (x^{5} cos (\frac{1}{x}))

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

d er i v a t i v e f (x) = lo g_{\frac{3}{2}} (x) + 2