derivative of ((x^2+2x-5)/((x+1)^2))

解答

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

\frac{12}{( x + 1 ) ^{3}}

求解步骤

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

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

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

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

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

化简

\frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{12}{( x + 1 ) ^{3}}

= \frac{12}{( x + 1 ) ^{3}}

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

d er i v a t i v e y = arcsin (\frac{1}{x})

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