(\partial)/(\partial x)(z*arctan(y/x))

解答

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

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

求解步骤

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

将

z, y

视为常数

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

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

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

t an g e n t y = x^{2}, (1, 1)

t an g e n t 6 x - x^{2}

in v erse l a pl a ce \frac{( 3 + 3 s )}{s ^{2} + 0.5}

d er i v a t i v e \frac{( cos ( x ) )}{1 - sin ( x )}

d er i v a t i v e \frac{2}{x + 3}