(\partial)/(\partial y)(xarcsin(y/x))

解答

\frac{\partial}{\partial y} (x arcsin (\frac{y}{x}))

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

求解步骤

\frac{\partial}{\partial y} (x arcsin (\frac{y}{x}))

将

x

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (arcsin (\frac{y}{x}))

使用连锁律:

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

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

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

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

化简

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

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

d er i v a t i v e f (x) = (x + 5) (9 x + 5)

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

\int (e^{- x^{2}}) d x

\int t e^{- t} d t

y^{^{''}} + 4 y^{^{'}} = - 6 x - 3