derivative (sqrt(x))/(x^2)

解答

导数

\frac{x}{x ^{2}}

- \frac{3}{2 x ^{\frac{5}{2}}}

求解步骤

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

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

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

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

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

化简

\frac{\frac{1}{2 x} x ^{2} - 2 x x}{( x ^{2} ) ^{2}} : - \frac{3}{2 x ^{\frac{5}{2}}}

= - \frac{3}{2 x ^{\frac{5}{2}}}

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

\frac{d}{d x} (x^{a r c t a n (x)})

\frac{d y}{d x} + 6 (tan (6 x)) y = 9 cos (6 x)

\frac{d}{d x} (8 x^{2} - x^{3})

\frac{d ^{2} y}{d x ^{2}} = \frac{1}{x} + 2