(\partial)/(\partial x)(ln((x+y)/(x-y)))

解答

\frac{\partial}{\partial x} (ln (\frac{x + y}{x - y}))

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

求解步骤

\frac{\partial}{\partial x} (ln (\frac{x + y}{x - y}))

将

y

视为常数

使用连锁律:

\frac{1}{\frac{x + y}{x - y}} \frac{\partial}{\partial x} (\frac{x + y}{x - y})

= \frac{1}{\frac{x + y}{x - y}} \frac{\partial}{\partial x} (\frac{x + y}{x - y})

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

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

化简

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

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

\int_{0}^{1} v^{2} cos (v^{3}) d v

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

\frac{d}{d x} (3 x^{2} - 4 x + 2)

\frac{d y}{d x} + y = e^{6 x}

\frac{d}{d x} (cos^{2} (sin (2 x)))