derivative of (10x/(1-x))

解答

\frac{d}{d x} (\frac{10 x}{1 - x})

\frac{10}{( 1 - x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{10 x}{1 - x})

将常数提出:

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

= 10 \frac{d}{d x} (\frac{x}{1 - x})

使用微分除法定则:

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

= 10 \cdot \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

= 10 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}}

化简

10 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}} : \frac{10}{( 1 - x ) ^{2}}

= \frac{10}{( 1 - x ) ^{2}}

\int \frac{3}{1 + 3 x} d x

\int_{0}^{5} \frac{7 t}{( t - 6 ) ^{2}} d t

t an g e n t f (x) = \frac{1}{x ^{3}}, (- 3, - \frac{1}{27})

\int \frac{t ^{2}}{( t ^{3} - 2 ) ^{5}} d t

n = 1 \sum \infty (1 - \frac{1}{3 n})^{n}