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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= - sin (\frac{x}{y}) \frac{1}{y}

Simplify

- sin (\frac{x}{y}) \frac{1}{y} : - \frac{sin ( \frac{x}{y} )}{y}

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

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