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Prove that derivative of tan^-1(x/(1+sqr...

Prove that derivative of `tan^-1(x/(1+sqrt(1-x^2)))` w.r.t `sin^-1` x is independent of x.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following w.r.t. as indicated: tan^-1((sqrt(1+x^2)...

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  2. Differentiate the following w.r.t. as indicated: tan^-1((sqrt(1+a^2x...

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  3. Prove that derivative of tan^-1(x/(1+sqrt(1-x^2))) w.r.t sin^-1 x is i...

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  4. Find dy/dx when y = tan^-1((4sqrtx)/(1-4xx))

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  5. Find dy/dx when y = tan^-1((sqrtx - sqrta)/(1+sqrtax))

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  6. Find dy/dx when tan^-1((sqrtx(3-x))/(1-3x))

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  7. Find (dy)/(dx), if y = tan^(-1) ((x^(1/3) + a^(1/3))/(1 - x^(1/3) a^(1...

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  8. Find dy/dx when y = cos^-1 (2x) + 2 cos^-1 sqrt(1-4x^2)

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  9. Differentiate the following functions w.r.t.x : tan^-1((a+bx)/(b-ax)...

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  10. Differentiate the following functions w.r.t.x : tan^-1((3-2x)/(1+6x)...

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  11. Differentiate the following functions w.r.t.x : cot^-1((3-2tanx)/(2+...

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  12. Differentiate the following functions w.r.t.x : tan^-1((5ax)/(a^2 - ...

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

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  14. If y = tan^-1 ((2x)/(1-x^2)) + sec^-1((1+x^2)/(1+x^2)), find dy/dx

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  15. Find dy/dx when y = sin^-1((2x)/(1+x^2)) + cos^-1 ((1-x^2)/(1+x^2)) wh...

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  16. Find dy/dx when y = sin^-1((2x)/(1+x^2)) + cos^-1 ((1-x^2)/(1+x^2)) wh...

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  17. Find dy/dx when y = sin^-1((2x)/(1+x^2)) + cos^-1 ((1-x^2)/(1+x^2)) wh...

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  18. Find dy/dx when y = sin^-1((2x)/(1+x^2)) + cos^-1 ((1-x^2)/(1+x^2)) wh...

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  19. If y = 2 tan^-1(sqrt((x-a)/(b-x))) and a < x < b, then show that (dy/d...

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  20. Differentiate cos^-1(1/(sqrt(1+t^2))) w.r.t sin^-1(t/(sqrt(1+t^2)))

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