derivative of (sqrt(2x-3)/(x^2))

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

\int \frac{81 + x ^{2}}{x} d x

x \to \infty lim (3 x^{3} + 3 x^{2} - x)

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n = 0 \sum \infty \frac{2 ^{n}}{1 ^{n}}

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