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

Lösung

ableitung von

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

\frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( x + 1 ) ( x - 1 ) ( x + 2 ) - ( 2 x + 1 ) ( x + 1 ) ^{2}}{( ( x - 1 ) ( x + 2 ) ) ^{2}} : \frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

= \frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

x \to \infty lim (x (x - x^{2} - 4))

t an g e n t 2 \frac{1}{x}, at x = 3

\int \frac{9 x ^{2} - 1}{x} d x

\int (1 - 2 e^{t a n (x)}) sec^{2} (x) d x

x \to 4 - lim (\frac{x + 2}{x - 4})