What is (\partial}{\partial x}(sin(\frac{2x)/y)) ?

The answer to (\partial}{\partial x}(sin(\frac{2x)/y)) is (2cos((2x)/y))/(y)

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(\partial}{\partial x}(sin(\frac{2x)/y))

\frac{\partial}{\partial x} (sin (\frac{2 x}{y}))

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

Solution steps

\frac{\partial}{\partial x} (sin (\frac{2 x}{y}))

Treat

y

as a constant

Apply the chain rule:

cos (\frac{2 x}{y}) \frac{\partial}{\partial x} (\frac{2 x}{y})

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

What is (\partial}{\partial x}(sin(\frac{2x)/y)) ?
The answer to (\partial}{\partial x}(sin(\frac{2x)/y)) is (2cos((2x)/y))/(y)