derivative ((3u^2))/((u^2+u)^3)

Lösung

ableitung von

\frac{( 3 u ^{2} )}{( u ^{2} + u ) ^{3}}

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

Schritte zur Lösung

\frac{d}{d u} (\frac{3 u ^{2}}{( u ^{2} + u ) ^{3}})

Entferne die Konstante:

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

= 3 \frac{d}{d u} (\frac{u ^{2}}{( u ^{2} + u ) ^{3}})

Wende die Quotientenregel an:

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

= 3 \cdot \frac{\frac{d}{d u} ( u ^{2} ) ( u ^{2} + u ) ^{3} - \frac{d}{d u} ( ( u ^{2} + u ) ^{3} ) u ^{2}}{( ( u ^{2} + u ) ^{3} ) ^{2}}

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

\frac{d}{d u} ((u^{2} + u)^{3}) = 3 (u^{2} + u)^{2} (2 u + 1)

= 3 \cdot \frac{2 u ( u ^{2} + u ) ^{3} - 3 ( u ^{2} + u ) ^{2} ( 2 u + 1 ) u ^{2}}{( ( u ^{2} + u ) ^{3} ) ^{2}}

Vereinfache

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

= \frac{3 ( - 4 u - 1 )}{u ^{2} ( u + 1 ) ^{4}}

\int_{1}^{2} \frac{3}{x ^{2}} - 1 d x

x \to 0 lim (\frac{x}{x})

s l o p e (3, 1), (5, - 4)

\int \frac{1}{9 x ^{2} - 36 x + 37} d x

\int \frac{x ^{7} e ^{x} - 4 x ^{6}}{x ^{7}} d x