derivative f(x)=(x+1)/(x-1)

解答

导数

f (x) = \frac{x + 1}{x - 1}

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

求解步骤

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

使用微分除法定则:

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

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

\frac{d}{d x} (x + 1) = 1

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

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

化简

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

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

e^{x}

y = 3 x + 2

y = x^{2} - 5 x

(- 5, 2), (4, - 7)

(3, 33)