derivative (7u^2)/((u^2+u)^3)

解答

导数

\frac{7 u ^{2}}{( u ^{2} + u ) ^{3}}

\frac{7 ( - 4 u - 1 )}{u ^{2} ( u + 1 ) ^{4}}

求解步骤

\frac{d}{d u} (\frac{7 u ^{2}}{( u ^{2} + u ) ^{3}})

将常数提出:

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

= 7 \frac{d}{d u} (\frac{u ^{2}}{( u ^{2} + u ) ^{3}})

使用微分除法定则:

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

= 7 \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)

= 7 \cdot \frac{2 u ( u ^{2} + u ) ^{3} - 3 ( u ^{2} + u ) ^{2} ( 2 u + 1 ) u ^{2}}{( ( u ^{2} + u ) ^{3} ) ^{2}}

化简

7 \cdot \frac{2 u ( u ^{2} + u ) ^{3} - 3 ( u ^{2} + u ) ^{2} ( 2 u + 1 ) u ^{2}}{( ( u ^{2} + u ) ^{3} ) ^{2}} : \frac{7 ( - 4 u - 1 )}{u ^{2} ( u + 1 ) ^{4}}

= \frac{7 ( - 4 u - 1 )}{u ^{2} ( u + 1 ) ^{4}}

\int \frac{3 x ^{2}}{1 - x ^{6}} d x

a re a x, x^{2} - 2

x \to 0 lim (3 cos (x))

a re a \frac{x ^{2}}{2} - 4 x + 6, \frac{x}{2} - 1, [0, 5]

d er i v a t i v e s (t) = t^{3} - 5 t + 8