derivative f(x)= 1/(sqrt(x))

解答

导数

f (x) = \frac{1}{x}

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

求解步骤

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

使用指数法则:

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

= \frac{d}{d 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}}}

s l o p e y = - \frac{1}{2} x + 3

s l o p e y = 5 x - 1

t an g e n t f (x) = ln (x) lo g_{2} (x), at x = 2

t an g e n t f (x) = \frac{1}{x ^{2}}

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