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

Lösung

ableitung von

\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}})

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}}

Vereinfache

\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}}

\frac{\partial}{\partial h} (2 π r^{2} + 2 π r h)

a re a f (x) = x^{5} + 2, g (x) = x + 2

d er i v a t i v e y = e^{x} ln (x)

\frac{\partial}{\partial x} (20 - 2 x + 1.5 - y + 3 a)

x \to - \infty lim (x \cdot e^{\frac{1}{x}})