derivative (sqrt(x))/(6+x)

解答

导数

\frac{x}{6 + x}

\frac{6 - x}{2 x ( 6 + x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{6 + 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 ) ( 6 + x ) - \frac{d}{d x} ( 6 + x ) x}{( 6 + x ) ^{2}}

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

\frac{d}{d x} (6 + x) = 1

= \frac{\frac{1}{2 x} ( 6 + x ) - 1 \cdot x}{( 6 + x ) ^{2}}

化简

\frac{\frac{1}{2 x} ( 6 + x ) - 1 \cdot x}{( 6 + x ) ^{2}} : \frac{6 - x}{2 x ( 6 + x ) ^{2}}

= \frac{6 - x}{2 x ( 6 + x ) ^{2}}

t an g e n t 9 x - 2 x^{2}

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

in v erse l a pl a ce \frac{4 s - 1}{s ^{2} ( s + 1 ) ^{3}}

x \to + 5 lim (\frac{x + 1}{x - 5})

\frac{d}{d x} ((x)^{3 x})