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Differentiate cos^(-1)(cosx),\ \ x in [0...

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

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given that,
`y= cos^(-1)(cosx) , x in [0,\ 2pi] `
`(dy)/(dx)= d/(dx) cos^(-1)(cosx)`
`=1/sqrt(1-cos^2x) (-sinx) `
`=-sinx/sqrt(1-cos^2x)`
`=-sinx/ sqrt (sin^2x)`
`=-sin x/sin x`
`=-1`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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  2. Differentiate sin^(-1)(sinx),\ \ x in [0,\ 2pi]

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  3. Differentiate cos^(-1)(cosx),\ \ x in [0,\ 2pi]

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  4. Differentiate tan^(-1)(tanx),\ \ x in [0,\ pi]-{pi/2}

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  5. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if -1/(sqrt(...

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  6. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if 1/(sqrt(2...

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  7. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x theta in [-(pi...

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  8. Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1/2ltxlt1/2

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  9. Differentiate sin^(-1)(3x-4x^3) with respect to x , if 1/2ltxlt1

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  10. Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1ltxlt-1/2

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  11. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0ltxlt1

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  12. Differentiate cos^(-1)(2x^2-1) with respect to x , if -1ltxlt0

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  13. Differentiate cos^(-1)(1-2x^2) with respect to x , if 0ltxlt1

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  14. Differentiate cos^(-1)(1-2x^2) with respect to x , if -1ltxlt0

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  15. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1/2,1/2)

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  16. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (1/2,\ 1)

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  17. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1,\ -1/2...

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  18. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x , if x in (-1,\...

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  19. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x , if x in (-oo,...

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  20. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x , if x in (1,\ ...

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