(\partial)/(\partial x)(1/(\sqrt[5]{x^4)})

解答

\frac{\partial}{\partial x} (\frac{1}{5 x ^{4}})

- \frac{4}{5 x ^{\frac{9}{5}}}

求解步骤

\frac{\partial}{\partial x} (\frac{1}{5 x ^{4}})

使用指数法则:

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

= \frac{\partial}{\partial x} ((x^{4})^{- \frac{1}{5}})

使用连锁律:

- \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \frac{\partial}{\partial x} (x^{4})

= - \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \frac{\partial}{\partial x} (x^{4})

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

= - \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \cdot 4 x^{3}

化简

- \frac{1}{5 ( x ^{4} ) ^{\frac{6}{5}}} \cdot 4 x^{3} : - \frac{4}{5 x ^{\frac{9}{5}}}

= - \frac{4}{5 x ^{\frac{9}{5}}}

in v erse l a pl a ce \frac{4}{( s + 2 ) ^{3}}

x \to 0 lim ((3 x + 1))

d er i v a t i v e f (x) = lo g_{10} (x)

\int \frac{x ^{2} + 2 x + 4}{( x + 1 ) ^{3}} d x

\int 5 tan^{2} (x) d x