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If y = 2 tan^-1(sqrt((x-a)/(b-x))) and a...

If `y = 2 tan^-1(sqrt((x-a)/(b-x)))` and a < x < b, then show that `(dy/dx)^2 + 1/((x-a)(x-b)) = 0`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find dy/dx when y = sin^-1((2x)/(1+x^2)) + cos^-1 ((1-x^2)/(1+x^2)) wh...

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

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

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

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

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  6. Differentiate sin^(-1)((2x)/(1+x^(2))) w. r. t. tan^(-1)x, -x lt x lt ...

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

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  8. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  9. Find dy/dx when y = sin^-1 (1/(sqrt(1+x^2))) + tan^-1 (sqrt(1+x^2)-1)/...

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

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  11. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

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  12. If y = 2/(sqrt(a^2 - b^2)) "tan"^(-1) (sqrt((a + b)/(a - b)) " tan " ...

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  13. Find dy/dx when xy = c^2

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  14. Find dy/dx when x^2 + y^2 = a^2

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  15. Find dy/dx when x^2/a^2- y^2/b^2 = 1

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  16. Find dy/dx when 2x^2 - 3xy + 4y^2 = 5

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  17. Find dy/dx when xy^2 - x^ 2y = 4

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  18. Find dy/dx when xy^3 - x^3 y = y

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  19. Find dy/dx when (x^2 +y^2))^2 = xy

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  20. Find dy/dx when sin(x+y) = 1/2

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