derivative of (10x/(x^2-6))

解答

\frac{d}{d x} (\frac{10 x}{x ^{2} - 6})

\frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{10 x}{x ^{2} - 6})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (\frac{x}{x ^{2} - 6})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 10 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) x}{( x ^{2} - 6 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 6) = 2 x

= 10 \cdot \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}}

化简

10 \cdot \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}} : \frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

= \frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

t an g e n t f (x) = x^{2} - 5, (- 3, 4)

\int (x - 3)^{2} \cdot e^{- x} d x

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\frac{d y}{d x} = y cos (3 x + 2)