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If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 ...

If `y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2)))` , then show that `(dy)/(dx) = x/(sqrt(1 - x^4))`

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION VI)(SHORT ANSWER TYPE QUESTIONS)
  1. Differentiate the following w.r.t.x. cos^(-1) (sin x)

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  2. Differentiate the following w.r.t.x. cot^(-1)((1 + cos x)/(sin x))

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  3. Differentiate the following w.r.t.x. tan^(-1)((sqrt(1 - cos 2x))/sqr...

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  4. Differentiate the following w.r.t.x. tan^(-1)((cos x - sin x)/(cos x...

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  5. Differentiate the following w.r.t.x. tan^(-1)(sec x + tan x)

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  6. Differentiate (x cos^(-1) x)/(sqrt(1 - x^2)) w.r.t.x.

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  7. Differentiate the following w.r.t.x. sin^(-1)(2xsqrt(1 - x^2))

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  8. Differentiate the following w.r.t.x. sin^(-1)(3x - 4x^3), - 1/2 lt x...

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  9. Differentiate the following w.r.t.x. cos^(-1)(4x^3 - 3x)

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  10. Differentiate the following w.r.t.x. cosec^(-1)(1 + x^2)/(2x)

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  11. Differentiate the following w.r.t.x. tan^(-1)((x)/(sqrt(a^2 - x^2)))

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  12. Differentiate the following w.r.t.x. tan^(-1)((x)/(1 + sqrt(1 - x^2)...

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  13. Differentiate the following w.r.t.x. tan^(-1) (sqrt(1 + x^2 )+ x)

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  14. Differentiate the following w.r.t.x. cot^(-1) (sqrt(1 + x^2) - x)

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  15. Differentiate sin^(-1)x + sin^(-1) sqrt(1 - x^2) w.r.t.x.

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  16. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

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  17. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  18. If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(d...

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  19. Differentiate tan^(-1) ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqr...

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  20. If sqrt(1 - x^6) + sqrt(1 - y^6) = a^3 (x^3 - y^3) prove that (dy)/(dx...

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