derivative of (x-sqrt(x)/(x+sqrt(x)))

解答

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

\frac{x}{( x + x ) ^{2}}

求解步骤

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

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

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

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

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

乘开

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

= \frac{x}{( x + x ) ^{2}}

\int \frac{1 + cos ( x )}{2} d x

n = 3 \sum \infty - \frac{5}{n ^{1.01}}

d er i v a t i v e f (x) = 7 x^{3} - 5 x + 8

d er i v a t i v e cos (3 t)

\frac{d}{d x} (\frac{10 x}{( x ^{2} + 1 ) ^{2}})