derivative of x/((1+x))

Lösung

\frac{d}{d x} (\frac{x}{( 1 + x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{( 1 + x )})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

\int \frac{x ^{2} + 3 x + 2}{x ^{2} ( x + 3 )} d x

\int \frac{a ^{t}}{t} d t

\int 6 sin^{3} (x) cos^{5} (x) d x

(x^{x})^{^{'}}

x \to 2 - lim (ln (4 - 2 x))