derivative 1/(9x^{8/9)}

解答

导数

\frac{1}{9 x ^{\frac{8}{9}}}

- \frac{8}{81 x ^{\frac{17}{9}}}

求解步骤

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{9} \frac{d}{d x} (\frac{1}{x ^{\frac{8}{9}}})

使用指数法则:

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

= \frac{1}{9} \frac{d}{d x} (x^{- \frac{8}{9}})

使用幂法则:

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

= \frac{1}{9} (- \frac{8}{9} x^{- \frac{8}{9} - 1})

化简

\frac{1}{9} (- \frac{8}{9} x^{- \frac{8}{9} - 1}) : - \frac{8}{81 x ^{\frac{17}{9}}}

= - \frac{8}{81 x ^{\frac{17}{9}}}

\frac{d}{d x} (\frac{1}{2} cos^{2} (5 x))

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

\frac{d y}{d x} = \frac{1}{x sin ( y ) + 2 sin ( 2 y )}

\int \frac{x}{x ^{2}} d x

x^{2} y^{^{'}} + x y = 3 y^{3}