d/(dy)(y/((x^2+y^2)^{3/2)})

解答

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

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

求解步骤

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

将

x

视为常数

使用微分除法定则:

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

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

\frac{d y}{d y} = 1

\frac{d}{d y} ((x^{2} + y^{2})^{\frac{3}{2}}) = 3 y (x^{2} + y^{2})^{\frac{1}{2}}

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

化简

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

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

(x^{3} + 3 x^{2} - 2 ln (x))^{^{'}}

\int_{1}^{2} \frac{- 9 ln ( x )}{x ^{2}} d x

\int (\frac{5 x ^{2} + x - 4}{x ^{2}}) d x

x \to 0 lim (x^{\frac{3}{2}})

l a pl a ce t r an s f or m e^{t - 7}