Differentiate sin^(-1)(sinx),\ \ x in [0...

Differentiate `sin^(-1)(sinx),\ \ x in [0,\ 2pi]`

Text Solution

Verified by Experts

given that,
`y= sin^(-1)(sinx) , x in [0,\ 2pi] `
`(dy)/(dx)= d/(dx) sin^(-1)(sinx)`
`=1/sqrt(1-sin^2x) cosx `
`=cosx/sqrt(1-sin^2x)`
`=cosx/ sqrt (cos^2x)`
`=cos x/cos x`
`=1`

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Differentiate x sin x

A

`sinx - x cos x `

B

`sinx + 2 x cosx`

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`sinx +x cos x`

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`sin2x-2xcosx`

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