derivative of 5/(\sqrt[3]{x^8})

解答

\frac{d}{d x} (\frac{5}{3 x ^{8}})

- \frac{40}{3 x ^{\frac{11}{3}}}

求解步骤

\frac{d}{d x} (\frac{5}{3 x ^{8}})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{3 x ^{8}})

使用指数法则:

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

= 5 \frac{d}{d x} ((x^{8})^{- \frac{1}{3}})

使用连锁律:

- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{8})

= - \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= 5 (- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \cdot 8 x^{7})

化简

5 (- \frac{1}{3 ( x ^{8} ) ^{\frac{4}{3}}} \cdot 8 x^{7}) : - \frac{40}{3 x ^{\frac{11}{3}}}

= - \frac{40}{3 x ^{\frac{11}{3}}}

\int \frac{cos ( 3 x )}{sin ^{2} ( 3 x )} d x

a re a x e^{x}, 1 \leq x \leq 7

\frac{\partial}{\partial x} (x^{2} y^{\frac{1}{3}})

\frac{d}{d t} (e^{- t} - e^{- t} t)

f (x) = e^{x c o s (x)}