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

The answer to (\partial)/(\partial y)(y+sin(x/y)) is 1-(xcos(x/y))/(y^2)

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (y) = 1

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

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

What is (\partial)/(\partial y)(y+sin(x/y)) ?
The answer to (\partial)/(\partial y)(y+sin(x/y)) is 1-(xcos(x/y))/(y^2)