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}}

t an g e n t f (x) = x^{2} + 6 x + 1, at x = - 2

p o l a r (- 4, 3)

d er i v a t i v e y = e^{e^{x}}

d er i v a t i v e x x + 1

mi d p o in t (1, - 6), (- 3, 4)