(\partial)/(\partial z)(yarctan(x/z))

解答

\frac{\partial}{\partial z} (y arctan (\frac{x}{z}))

- \frac{y x}{x ^{2} + z ^{2}}

求解步骤

\frac{\partial}{\partial z} (y arctan (\frac{x}{z}))

将

y, x

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial z} (arctan (\frac{x}{z}))

使用连锁律:

\frac{1}{( \frac{x}{z} ) ^{2} + 1} \frac{\partial}{\partial z} (\frac{x}{z})

= \frac{1}{( \frac{x}{z} ) ^{2} + 1} \frac{\partial}{\partial z} (\frac{x}{z})

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

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

化简

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

= - \frac{y x}{x ^{2} + z ^{2}}

\int (7 + 2 x) e^{x} d x

\int \frac{( x + 1 ) ^{2}}{x ^{2} + 1} d x

\int_{0}^{π} sin (4 x) d x

t an g e n t y = - 2 x^{2}, (- 5, 50)

a re a y = \frac{1}{2} x^{2} + 1, (0, 1)