(\partial)/(\partial y)(cos(x/y))

解答

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

\frac{x sin ( \frac{x}{y} )}{y ^{2}}

求解步骤

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

将

x

视为常数

使用连锁律:

- sin (\frac{x}{y}) \frac{\partial}{\partial y} (\frac{x}{y})

= - sin (\frac{x}{y}) \frac{\partial}{\partial y} (\frac{x}{y})

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

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

化简

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

= \frac{x sin ( \frac{x}{y} )}{y ^{2}}

s im pl i f y \frac{x ^{3}}{16 - x ^{2}} d x

\frac{d}{d x} (8^{x^{8}})

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

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\int e^{- 0.4 x} d x