derivative of (x^2/(x+10))

解答

\frac{d}{d x} (\frac{x ^{2}}{x + 10})

\frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2}}{x + 10})

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 + 10 ) - \frac{d}{d x} ( x + 10 ) x ^{2}}{( x + 10 ) ^{2}}

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

\frac{d}{d x} (x + 10) = 1

= \frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}}

化简

\frac{2 x ( x + 10 ) - 1 \cdot x ^{2}}{( x + 10 ) ^{2}} : \frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

= \frac{x ^{2} + 20 x}{( x + 10 ) ^{2}}

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

\int \frac{x ^{2} + 5 x - 8}{x} d x

x \to \infty lim (2 x + 8)

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

x \to 2 lim (a^{2} x + 2 a)