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

解答

导数

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

化简

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

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

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

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

s l o p e 5

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

mi d p o in t (7, - 5), (9, - 1)