derivative y=(x^2-4)/(x-3)

解答

导数

y = \frac{x ^{2} - 4}{x - 3}

\frac{x ^{2} - 6 x + 4}{( x - 3 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2} - 4}{x - 3})

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} - 4 ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( x ^{2} - 4 )}{( x - 3 ) ^{2}}

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

\frac{d}{d x} (x - 3) = 1

= \frac{2 x ( x - 3 ) - 1 \cdot ( x ^{2} - 4 )}{( x - 3 ) ^{2}}

化简

\frac{2 x ( x - 3 ) - 1 \cdot ( x ^{2} - 4 )}{( x - 3 ) ^{2}} : \frac{x ^{2} - 6 x + 4}{( x - 3 ) ^{2}}

= \frac{x ^{2} - 6 x + 4}{( x - 3 ) ^{2}}

\frac{d}{d x} ((sec (x) + tan (x))^{- 3})

\int_{0}^{4} 5 x d x

x \to 0 + lim (ln (tan (x)))

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\int \frac{1}{2 y - y ^{2}} d y