derivative f(x)=(x^2)/(x-11)

解答

导数

f (x) = \frac{x ^{2}}{x - 11}

\frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2}}{x - 11})

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 - 11 ) - \frac{d}{d x} ( x - 11 ) x ^{2}}{( x - 11 ) ^{2}}

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

\frac{d}{d x} (x - 11) = 1

= \frac{2 x ( x - 11 ) - 1 \cdot x ^{2}}{( x - 11 ) ^{2}}

化简

\frac{2 x ( x - 11 ) - 1 \cdot x ^{2}}{( x - 11 ) ^{2}} : \frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

= \frac{x ^{2} - 22 x}{( x - 11 ) ^{2}}

d er i v a t i v e 5 x^{3} + 2 x^{2} + 3

x \to \infty lim (co x (x))

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