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

If `y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2))` , prove that `(dy)/(dx) = 4/(1 + x^2)` , 0 < x < 1

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following functions w.r.t.x : cot^-1((3-2tanx)/(2+...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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