derivative f(x)=(3-x)/(x+1)

解答

导数

f (x) = \frac{3 - x}{x + 1}

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

求解步骤

\frac{d}{d x} (\frac{3 - x}{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} ( 3 - x ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( 3 - x )}{( x + 1 ) ^{2}}

\frac{d}{d x} (3 - x) = - 1

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

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

化简

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

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

\frac{d}{d x} (e^{- x} cos (5 x))

s l o p e (8 \frac{1}{7}, 9), (4, 3.2)

x \to 0 lim (\frac{( 3 e ^{- x} - 3 )}{x ^{2} - 2 x})

d er i v a t i v e y = sin^{2} (x) - cos^{2} (x)

x \to - 35 lim (34 + x)