derivative (2x^2+4x)/((x+1)^2)

Lösung

ableitung von

\frac{2 x ^{2} + 4 x}{( x + 1 ) ^{2}}

\frac{4}{( x + 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} + 4 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} ( 2 x ^{2} + 4 x ) ( x + 1 ) ^{2} - \frac{d}{d x} ( ( x + 1 ) ^{2} ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{2} + 4 x) = 4 x + 4

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

= \frac{( 4 x + 4 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}}

Vereinfache

\frac{( 4 x + 4 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( 2 x ^{2} + 4 x )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{4}{( x + 1 ) ^{3}}

= \frac{4}{( x + 1 ) ^{3}}

\frac{d y}{d x} + \frac{1}{x} y = \frac{1}{y}

\int_{- \infty}^{- 4} x e^{x} d x

t an g e n t f (x) = x^{2} - 2, (2, 2)

\frac{d}{d x} (5 x arcsin (x))

x \to \infty lim (0, x)