derivative of (x^2/(sqrt(x^4+x^2+1)))

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

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

y^{3} - (10 x + 4) + 3 x y^{2} y^{^{'}} = 0

d er i v a t i v e (3 a + 1)^{2}

\int_{1}^{9} x ln (x) d x

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