derivative of 1/(sqrt(2x))

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

in v erse l a pl a ce \frac{1}{( s ( s ^{2} + 6 s - 27 ) )}

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

d er i v a t i v e \frac{3 x - 1}{( x - 1 ) ^{3}}

\int 6 x + 2 d x

d er i v a t i v e (x + 2)^{3} - e^{3 x}