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)

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derivative of

y = sin (x^{- 1})

- \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}}

x^{2} cos (lo g_{10} (x))

\frac{d}{d t} (2 t - 2)

\frac{d}{d a} (sec^{2} (a) + tan^{2} (a))

y = 5 sin (x) + 3 cos (x) + 5 x^{2}

\frac{d}{d n} (i^{4 n + 1})

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)