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Popular >

derivative of sin(pi/x)

Solution

\frac{d}{d x} (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

(\partial)/(\partial x)(ln(x^3+y^7))

\frac{\partial}{\partial x} (ln (x^{3} + y^{7}))

derivative of sin^{-5}(x-cos^3(x))

\frac{d}{d x} (sin^{- 5} (x) - cos^{3} (x))

integral of ((x+1))/(sqrt(x))

\int \frac{( x + 1 )}{x} d x

(csc^{2} (x))^{^{'}}

integral of x/(sqrt(25-x^2))

\int \frac{x}{25 - x ^{2}} 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)