derivative y=(a-x)/(a+x)

解答

导数

y = \frac{a - x}{a + x}

- \frac{2 a}{( a + x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{a - x}{a + x})

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

\frac{d}{d x} (a - x) = - 1

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

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

化简

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

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

\frac{d y}{d x} - \frac{y}{x} = \frac{x}{y}

a re a x, \frac{1}{2} x, x = 9

\frac{\partial}{\partial x} (- x e^{3 x y})

\int_{- 1}^{5} (3 e^{- x})^{2} d x

\int \frac{2 x}{3 9 - x ^{2}} d x