derivative of ((x^5-5)/(x+1))

解答

\frac{d}{d x} (\frac{( x ^{5} - 5 )}{x + 1})

\frac{4 x ^{5} + 5 x ^{4} + 5}{( x + 1 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{( x ^{5} - 5 )}{x + 1})

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 ^{5} - 5 ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x ^{5} - 5 )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x^{5} - 5) = 5 x^{4}

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

= \frac{5 x ^{4} ( x + 1 ) - 1 \cdot ( x ^{5} - 5 )}{( x + 1 ) ^{2}}

化简

\frac{5 x ^{4} ( x + 1 ) - 1 \cdot ( x ^{5} - 5 )}{( x + 1 ) ^{2}} : \frac{4 x ^{5} + 5 x ^{4} + 5}{( x + 1 ) ^{2}}

= \frac{4 x ^{5} + 5 x ^{4} + 5}{( x + 1 ) ^{2}}

\int_{1}^{2} (2 x^{2} - 2) d x

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d er i v a t i v e f (x) = x - 4