derivative of (sqrt(x)-2/(\sqrt[3]{x)})

解答

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

\frac{x + 4}{6 x ^{\frac{4}{3}}}

求解步骤

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

\frac{d}{d x} (x - 2) = \frac{1}{2 x}

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

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

化简

\frac{\frac{1}{2 x} 3 x - \frac{1}{3 x ^{\frac{2}{3}}} ( x - 2 )}{( 3 x ) ^{2}} : \frac{x + 4}{6 x ^{\frac{4}{3}}}

= \frac{x + 4}{6 x ^{\frac{4}{3}}}

\frac{d}{d s} (\frac{s}{s ^{2} + 25})

\int (4 x + 3)^{7} d x

\int \frac{17}{17 + e ^{x}} d x

\int_{0}^{\infty} x e^{- 5 x} d x

x \to - 1 lim ((sin (\frac{π}{2}) x + 2^{- 3 x})^{2})