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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

\int \frac{x}{x ^{2} - 2 x + 1} d x

\int_{0}^{3} 2^{x} d x

n = 0 \sum \infty \frac{n ^{3}}{2 ^{n}}

\int \frac{1}{sin ^{2} ( a ) x} d x

5 x - 2 x

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