derivative (8x)/(1-x)

解答

导数

\frac{8 x}{1 - x}

\frac{8}{( 1 - x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{8 x}{1 - x})

将常数提出:

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

= 8 \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}}

= 8 \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

= 8 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}}

化简

8 \cdot \frac{1 \cdot ( 1 - x ) - ( - 1 ) x}{( 1 - x ) ^{2}} : \frac{8}{( 1 - x ) ^{2}}

= \frac{8}{( 1 - x ) ^{2}}

l a pl a ce t r an s f or m - 2 t + 8

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

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

\frac{d x}{d t} = 12 - \frac{x}{200 + 3 t}

t an g e n t f (x) = x^{3} - 3 x^{2} - 9 x + 27, at x = 4