What is (\partial)/(\partial y)(cos(x/y)) ?

The answer to (\partial)/(\partial y)(cos(x/y)) is (xsin(x/y))/(y^2)

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

- 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}})

Simplify

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

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

\frac{x ^{3}}{16 - x ^{2}} d x

\int \frac{5}{2 x} d x

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

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

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

What is (\partial)/(\partial y)(cos(x/y)) ?
The answer to (\partial)/(\partial y)(cos(x/y)) is (xsin(x/y))/(y^2)