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

解答

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

\frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

求解步骤

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

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

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

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

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

化简

\frac{2 x ( x + 4 ) - 1 \cdot x ^{2}}{( x + 4 ) ^{2}} : \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

= \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

s l o p e in t erce pt (15, 0), (0, - 2)

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