derivative \sqrt[3]{4x-5}

解答

导数

3 4 x - 5

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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