derivative y=(sqrt(x))/(3+x)

解答

导数

y = \frac{x}{3 + x}

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

求解步骤

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

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

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

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

化简

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

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

\int - \frac{3}{x ^{3}} d x

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

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

in v erse l a pl a ce \frac{1}{( s \cdot ( s + 1 ) )}

\int \frac{x ^{2}}{16 + 9 x ^{2}} d x