derivative (sqrt(x)-1)/(sqrt(x)+1)

解答

导数

\frac{x - 1}{x + 1}

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

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

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

化简

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

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

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

\int x \cdot (4 - x) d x

l a pl a ce t r an s f or m 5 + 4 δ (t)

\int 4^{s i n (x)} cos (x) d x

x \to - 7 lim (\frac{x + 8}{x + 7})