derivative of (sqrt(x)/(x^3+1))

解答

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

\frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

求解步骤

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

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

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

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

化简

\frac{\frac{1}{2 x} ( x ^{3} + 1 ) - 3 x ^{2} x}{( x ^{3} + 1 ) ^{2}} : \frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

= \frac{- 5 x ^{3} + 1}{2 x ( x ^{3} + 1 ) ^{2}}

x \to 2 + lim (2 x - 2)

t an g e n t y = sin (sin (x)), (π, 0)

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\frac{\partial}{\partial u} ((u^{2} v - v^{3})^{5})

\int x y sin (z) d z