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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Streiche

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

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

t an g e n t f (x) = \frac{x}{x ^{2} + 9}, at x = 0

d er i v a t i v e y = 3 x^{2} - 4

\int_{5}^{6} \frac{x}{x ^{2} + 6 x + 13} d x

d er i v a t i v e e^{a x} sin (b x)

\frac{\partial}{\partial y} (e^{2 x} cos (y))