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

The answer to (\partial)/(\partial x)(x/y-sin(y)) is 1/y

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

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

\frac{1}{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (sin (y)) = 0

= \frac{1}{y} - 0

Simplify

= \frac{1}{y}

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