derivative of (2x^{3/2}-x^2+4/x)

解答

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

\frac{- x ^{2} + x ^{\frac{3}{2}} - 4}{x ^{2}}

求解步骤

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

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

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

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

化简

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

= \frac{- x ^{2} + x ^{\frac{3}{2}} - 4}{x ^{2}}

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{2}{x ^{3}})

\int_{- 1}^{1} 2 - 2 x^{2} d x

y^{^{''}} + 2 y^{^{'}} + y = x^{2} e^{- x}

f (x) = arcsin (x^{2})

n = 1 \sum \infty \frac{n}{2 n}