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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - \frac{29}{x ^{30}} d x

e^{- t} cos (t)

y^{^{''}} + y = 4 csc^{2} (x)

3 x d y + 2 y d x = 0

\int \frac{3 x ^{3} + 9 x ^{2} + 9 x + 4}{x ^{2} + 3 x + 2} d x

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