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

The answer to (\partial)/(\partial y)(sin(x/y)) is -(xcos(x/y))/(y^2)

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(\partial)/(\partial y)(sin(x/y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x^{2} - 13 d x

\frac{d}{d x} (- \frac{20000}{1 + 0.2 x})

\frac{d}{d x} (csc^{3} (3 - x))

\int \frac{8 x + 1}{( 4 x ^{2} + x ) ^{6}} d x

\int \frac{1}{x lo g _{x} ( x )} d x

What is (\partial)/(\partial y)(sin(x/y)) ?
The answer to (\partial)/(\partial y)(sin(x/y)) is -(xcos(x/y))/(y^2)