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If y = sqrt(x+ sqrt(x + sqrt(x + ......o...

If `y = sqrt(x+ sqrt(x + sqrt(x + ......oo)))`, show that `(2y - 1) (dy)/(dx) = 1`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If sqrt(1-x^2) + sqrt(1-y^2) = a(x-y), show that dy/dx = sqrt((1-y^2)/...

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  2. If sqrt(1-x^6)+sqrt(1-y^6)=a^3(x^3-y^3), prove that : dy/dx = x^2/y^2s...

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  3. If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))), show that (2y - 1) (dy)/...

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  4. y = sqrt(tan x + sqrt(tanx + sqrt(tanx + ...."to" oo))) prove that (2y...

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  5. Differentiate the following functions w.r.t.x : (x+1)^2 (x+2)^3 (x+3)^...

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  6. Differentiate the following functions w.r.t.x : sqrt((x-1)(x-2)(x-3)(x...

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  7. Differentiate the following functions w.r.t.x : e^x cos^3 x sin^4 x

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  8. Differentiate the following functions w.r.t.x : x^2 e^x sin x

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  9. Differentiate the following functions w.r.t.x : (2x+1)^(1//2) (3x +2)^...

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  10. Differentiate the following functions w.r.t.x : e^x cos^3 x sin^4 x

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  11. Differentiate the following w.r.t. x : cos x . Cos 2x. Cos 3x

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  12. Differentiate the following w.r.t. x: (sinx)^(cos^-1x)

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  13. Find (dy)/(dx) when x^y + y^x = a^b

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  14. Find dy/dx when x^ y =1

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  15. Find dy/dx when xy = e^(x-y)

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  16. Differentiate the following functions w.r.t.x : x^x

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  17. Differentiate the following functions w.r.t.x : (sinx)^x

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  18. Differentiate the following functions w.r.t.x : (2x+3)^(x-5)

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  19. Differentiate the following functions w.r.t.x : x^(sin^-1x)

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  20. Differentiate the following functions w.r.t.x : x^(sinx) + sinx^(cos...

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