derivative of (2x^2-1/(x^2-3))

解答

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

- \frac{10 x}{( x ^{2} - 3 ) ^{2}}

求解步骤

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

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

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

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

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

化简

\frac{4 x ( x ^{2} - 3 ) - 2 x ( 2 x ^{2} - 1 )}{( x ^{2} - 3 ) ^{2}} : - \frac{10 x}{( x ^{2} - 3 ) ^{2}}

= - \frac{10 x}{( x ^{2} - 3 ) ^{2}}

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