derivative y=(-12)/(\sqrt[3]{x)}

解答

导数

y = \frac{- 12}{3 x}

\frac{4}{x ^{\frac{4}{3}}}

求解步骤

\frac{d}{d x} (\frac{- 12}{3 x})

化简

\frac{- 12}{3 x} : - \frac{12}{3 x}

= \frac{d}{d x} (- \frac{12}{3 x})

将常数提出:

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

= - 12 \frac{d}{d x} (\frac{1}{3 x})

使用指数法则:

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

= - 12 \frac{d}{d x} (x^{- \frac{1}{3}})

使用幂法则:

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

= - 12 (- \frac{1}{3} x^{- \frac{1}{3} - 1})

化简

- 12 (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : \frac{4}{x ^{\frac{4}{3}}}

= \frac{4}{x ^{\frac{4}{3}}}

d er i v a t i v e f (x) = \frac{3 cos ( x )}{3 x ^{2} + 3 x - 1}

\frac{d}{d x} (ln (c x))

\frac{d}{d x} (a r (x) c, (ln (x)))

\int x (x^{2} - 2) d x

d er i v a t i v e \frac{1}{4 x ^{2} + 5 x}