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Popular >

derivative of sin(pi/x)

Solution

derivative of

sin (\frac{π}{x})

Solution

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

Solution steps

\frac{d}{d x} (sin (\frac{π}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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\int x^{2} + 2 x + 5 d x

Frequently Asked Questions (FAQ)

What is the derivative of sin(pi/x) ?
The derivative of sin(pi/x) is -(picos(pi/x))/(x^2)
What is the first derivative of sin(pi/x) ?
The first derivative of sin(pi/x) is -(picos(pi/x))/(x^2)