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Popular >

derivative of cos(pi/x)

Solution

\frac{d}{d x} (cos (\frac{π}{x}))

Solution

\frac{π sin ( \frac{π}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (cos (\frac{π}{x}))

Apply the chain rule:

- sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

= - sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

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

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

Simplify

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

= \frac{π sin ( \frac{π}{x} )}{x ^{2}}

Popular Examples

integral from 2 to infinity of-8x^{-2}

\int_{2}^{\infty} - 8 x^{- 2} d x

limit as x approaches 0 of (cos(3x))/x

x \to 0 lim (\frac{cos ( 3 x )}{x})

derivative of e^{-x}cos(sqrt(x))

\frac{d}{d x} (e^{- x} cos (x))

(dy)/(dx)=(y^2+1)/(x^2+1)

\frac{d y}{d x} = \frac{y ^{2} + 1}{x ^{2} + 1}

parity y=cos(tan(x))parity

y = cos (tan (x))

Frequently Asked Questions (FAQ)

What is the derivative of cos(pi/x) ?
The derivative of cos(pi/x) is (pisin(pi/x))/(x^2)
What is the first derivative of cos(pi/x) ?
The first derivative of cos(pi/x) is (pisin(pi/x))/(x^2)