(\partial)/(\partial x)(1/(sqrt(x)))

解答

\frac{\partial}{\partial x} (\frac{1}{x})

- \frac{1}{2 x ^{\frac{3}{2}}}

求解步骤

\frac{\partial}{\partial x} (\frac{1}{x})

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

化简

- \frac{1}{2} x^{- \frac{1}{2} - 1} : - \frac{1}{2 x ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}}

\int - e^{4 x} + 4 x^{5} d x

t an g e n t f (x) = x, at x = 36

d er i v a t i v e f (x) = 4 x^{3} + 9

(- x^{- 2})^{^{'}}

(x^{2} + 2 x - 1) y^{^{'}} - (x + 1) y = x - 1