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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 1 lim (∣ 3 x - 6 ∣)

\frac{d}{d x} (ln (5 x^{3}))

\int 38 arctan (x) d x

x \to 0 lim (\frac{e ^{x} - 1}{10 x})

\frac{\partial}{\partial z} (yz)