derivative of (x^2/((1+x)^5))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{( 1 + x ) ^{5}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{( 1 + x ) ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + x ) ^{5} - \frac{d}{d x} ( ( 1 + x ) ^{5} ) x ^{2}}{( ( 1 + x ) ^{5} ) ^{2}}

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

\frac{d}{d x} ((1 + x)^{5}) = 5 (1 + x)^{4}

= \frac{2 x ( 1 + x ) ^{5} - 5 ( 1 + x ) ^{4} x ^{2}}{( ( 1 + x ) ^{5} ) ^{2}}

Vereinfache

\frac{2 x ( 1 + x ) ^{5} - 5 ( 1 + x ) ^{4} x ^{2}}{( ( 1 + x ) ^{5} ) ^{2}} : \frac{x ( - 3 x + 2 )}{( 1 + x ) ^{6}}

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

\frac{d}{d x} (cos (x - y) + ln (x + y))

\int \frac{2 x ^{3} - x ^{2} + 2 x + 4}{1 + x ^{2}} d x

\int (8 x + 3) 4 x^{2} + 3 x d x

\frac{d}{d x} (\frac{x ^{2} + 13 x + 36}{x ^{2} + 8 x - 9})

d er i v a t i v e 9 x^{\frac{2}{3}}