(\partial)/(\partial y)(arcsin(x/y))

解答

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

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

求解步骤

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

将

x

视为常数

使用连锁律:

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

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

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

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

化简

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

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

\frac{d}{d x} (5 2 - x^{2})

t a y l or e^{x^{2} + x}

\frac{d}{d x} (y^{2} - x)

s im pl i f y e^{l n (s i n (x^{2}))} 2 x + 1

x \to 0 lim (\frac{ln ( x + 1 )}{x})