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

解答

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

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

求解步骤

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

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

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

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

化简

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

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

x \to 0 lim (e^{2 x} + 10 x)

d er i v a t i v e \frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

\frac{\partial}{\partial x} (arctan (x^{4} y^{3}))

f (x) = e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

k = 1 \sum \infty \frac{3 ^{k}}{k !}