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}}

\frac{d}{d x} (\frac{6}{( 1 + x ) ^{4}})

\frac{d}{d x} (\frac{6 x ^{3} - 2}{x ^{2} - 4})

f (x) = x^{2} + x

\int sec (5 x) tan (5 x) d x

\frac{d}{d x} (sec (\frac{1}{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)