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

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

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(\partial)/(\partial y)(xsin(x/y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

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}}

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

Simplify

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

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

\int x sin (3 a x) d x

\frac{\partial}{\partial x} (x ln (z^{4} + x^{3}))

f (x) = (\frac{x + 3}{x - 3})^{2}, at x = 4

\frac{d}{d x} (ln (\frac{( 1 - x )}{1 + x}))

\int_{1}^{9} π (x - 1)^{2} d x

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