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Popular Calculus >

derivative of y=sin(x^{-1})

Solution

derivative of

y = sin (x^{- 1})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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