d/(d{y)}(({y})/({y)+c/({y)}})

解答

\frac{d}{d y} (\frac{y}{y + \frac{c}{y}})

\frac{2 c y}{( y ^{2} + c ) ^{2}}

求解步骤

\frac{d}{d y} (\frac{y}{y + \frac{c}{y}})

使用微分除法定则:

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

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

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

\frac{d}{d y} (y + \frac{c}{y}) = 1 - \frac{c}{y ^{2}}

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

化简

\frac{1 \cdot ( y + \frac{c}{y} ) - ( 1 - \frac{c}{y ^{2}} ) y}{( y + \frac{c}{y} ) ^{2}} : \frac{2 c y}{( y ^{2} + c ) ^{2}}

= \frac{2 c y}{( y ^{2} + c ) ^{2}}

\int - \frac{7}{x ^{2} + 16} d x

t an g e n t f (x) = \frac{1}{2 x}, at x = 64

\frac{d}{d x} (cos (x + π))

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

\int sec^{3} (4 x) tan (4 x) d x