derivative (\sqrt[3]{x^2+3})/x

解答

导数

\frac{3 x ^{2} + 3}{x}

\frac{2 x ^{2} - 3 3 x ^{2} + 3 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{3 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}}}

求解步骤

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

化简

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

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

f^{^{'}} (x) = sin (4) (4 x^{5})

d er i v a t i v e 9 (x - 4)^{\frac{2}{3}}

\frac{d}{d x} (210)

\frac{d}{d x} (\frac{e ^{- x^{2}}}{x ^{3}})

d er i v a t i v e ln (6 - x^{2} + 2 x^{4})