derivative of (27/((x+5)^{4/3)})

解答

\frac{d}{d x} (\frac{27}{( x + 5 ) ^{\frac{4}{3}}})

- \frac{36}{( x + 5 ) ^{\frac{7}{3}}}

求解步骤

\frac{d}{d x} (\frac{27}{( x + 5 ) ^{\frac{4}{3}}})

将常数提出:

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

= 27 \frac{d}{d x} (\frac{1}{( x + 5 ) ^{\frac{4}{3}}})

使用指数法则:

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

= 27 \frac{d}{d x} ((x + 5)^{- \frac{4}{3}})

使用连锁律:

- \frac{4}{3 ( x + 5 ) ^{\frac{7}{3}}} \frac{d}{d x} (x + 5)

= - \frac{4}{3 ( x + 5 ) ^{\frac{7}{3}}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= 27 (- \frac{4}{3 ( x + 5 ) ^{\frac{7}{3}}} \cdot 1)

化简

27 (- \frac{4}{3 ( x + 5 ) ^{\frac{7}{3}}} \cdot 1) : - \frac{36}{( x + 5 ) ^{\frac{7}{3}}}

= - \frac{36}{( x + 5 ) ^{\frac{7}{3}}}

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