derivative f(x)=(x^2+2x-6)/((x+1)^2)

Lösung

ableitung von

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

\frac{14}{( x + 1 ) ^{3}}

Schritte zur Lösung

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

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

Vereinfache

\frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 6 )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{14}{( x + 1 ) ^{3}}

= \frac{14}{( x + 1 ) ^{3}}

x \to 0 - lim (e^{\frac{5}{x}})

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

\frac{\partial}{\partial y} (x^{3} + y^{2})

x \to 5 - lim (\frac{1}{x - 5})

\frac{d}{d x} (m x)