derivative of (-5/(\sqrt[4]{x^3)})

解答

\frac{d}{d x} (\frac{- 5}{4 x ^{3}})

\frac{15}{4 x ^{\frac{7}{4}}}

求解步骤

\frac{d}{d x} (\frac{- 5}{4 x ^{3}})

化简

\frac{- 5}{4 x ^{3}} : - \frac{5}{4 x ^{3}}

= \frac{d}{d x} (- \frac{5}{4 x ^{3}})

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \frac{d}{d x} (x^{3})

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

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

= - 5 (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2})

化简

- 5 (- \frac{1}{4 ( x ^{3} ) ^{\frac{5}{4}}} \cdot 3 x^{2}) : \frac{15}{4 x ^{\frac{7}{4}}}

= \frac{15}{4 x ^{\frac{7}{4}}}

in v erse l a pl a ce \frac{5 s + 5}{s ( s ^{2} + 6 s + 10 )}

x \to - 1 lim (- \frac{2}{( x + 1 ) ^{2}})

\frac{d}{d y} (x - y)

in v erse l a pl a ce \frac{2}{s + 1} + \frac{24 s}{s ^{2} + 9}

f^{^{''}} (x) = 4, f^{^{'}} (2) = 10, f (2) = 15