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

解答

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

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

求解步骤

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

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

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

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

化简

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

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

\int \frac{1}{cos ^{2} ( x ) tan ( x )} d x

\int_{0}^{π} 5 x cos (x^{2}) d x

n = 1 \sum \infty \frac{e ^{n}}{n !}

y^{^{''}} + 16 y = 16 cos (4 x)

d er i v a t i v e f (x) = 2 π