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Differentiate cos^(-1)(1-2x^2) with resp...

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

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Verified by Experts

Given that,
`y=cos^(-1)(1-2x^2)`
`x= sin theta`
`=>y=cos^-1(1-2sin^2theta)`
`=>y=cos^-1 (cos 2theta)`
`0ltxlt1`
or `0ltsin theta lt1`
or `0 lt theta lt pi/2`
or `0 lt 2theta lt pi`
`y= 2theta`
`y=2 sin^-1 x`
`(dy)/(dx)=2/sqrt(1-x^2)`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0ltxlt1

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

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

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

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

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

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

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

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

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

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  11. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if -1/(sqrt(3))ltxlt1/(sqr...

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  12. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if x >1/(sqrt(3))

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  13. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if x<-1/(sqrt(3))

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  14. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (-1...

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  15. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (1,...

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  16. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to x , when x in (-o...

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  17. Differentiate cos^(-1)((1-x^2)/(1+x^2)) with respect to x , when x in ...

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  18. Differentiate cos^(-1)((1-x^2)/(1+x^2)) with respect to x , when x in ...

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  19. Differentiate cos^(-1)((1-x^2)/(1+x^2)), 0lt xlt1 with respect to x

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  20. Differentiate sin^(-1)((1-x^2)/(1+x^2)), 0ltxlt1 with respect to x

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