What is the derivative of y=sin(1/x) ?

The derivative of y=sin(1/x) is -(cos(1/x))/(x^2)

What is the first derivative of y=sin(1/x) ?

The first derivative of y=sin(1/x) is -(cos(1/x))/(x^2)

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derivative

- \frac{cos ( \frac{1}{x} )}{x ^{2}}

Solution steps

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

Apply the chain rule:

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

= cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= cos (\frac{1}{x}) (- \frac{1}{x ^{2}})

Simplify

cos (\frac{1}{x}) (- \frac{1}{x ^{2}}) : - \frac{cos ( \frac{1}{x} )}{x ^{2}}

= - \frac{cos ( \frac{1}{x} )}{x ^{2}}

What is the derivative of y=sin(1/x) ?
The derivative of y=sin(1/x) is -(cos(1/x))/(x^2)
What is the first derivative of y=sin(1/x) ?
The first derivative of y=sin(1/x) is -(cos(1/x))/(x^2)