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

If `log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2)`, show that `(1 - x^2) (dy)/(dx) + xy + 1 = 0`

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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION V)(SHORT ANSWER TYPE QUESTIONS)
  1. Find (dy)/(dx) in the following : y + sin y = cos x

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  2. Find dy/dx in the following: 2x+3y= sinx

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  3. Find (dy)/(dx) in the following : x^3 + y^3 +3a xx y = 0

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  4. Find (dy)/(dx) in the following : x^2 + y^4 + 4xy = 100

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  5. Find (dy)/(dx) in the following : x^6 + y^6 + 6x^2 y^2 = 16

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  6. Find (dy)/(dx) in the following : x^2 + y^2 + 2yx + 2 + y + c = 0

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  7. Find (dy)/(dx) in the following : ax^2 + 2hxy + by^2 + 2gx + 2 + y +...

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  8. Find (dy)/(dx) in the following : x^3 + y^3 = sin (x + y)

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  9. Find (dy)/(dx) in the following : x^3y + y^3 x = a^4

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  10. Find (dy)/(dx) in the following : (x^2 + y^2)^2 = xy

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  11. Find (dy)/(dx) in the following : x^(2//3) + y^(2//3) = a^(2//3)

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  12. Find (dy)/(dx) in the following : y sec x + tan x + x^2 y = 0

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  13. If e^x + e^y = e^(x +y) , prove that (dy)/(dx) = (e^x (e^y - 1))/(e^y ...

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  14. If log (sqrt(1 + x^2) - x) = y sqrt(1 + x^2), show that (1 - x^2) (dy)...

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  15. If x^2 + 2xy + y^2 = 18 , verify that (dy)/(dx) xx (dx)/(dy) = 1

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  16. If siny = xsin(a+y), prove that dy/dx=sin^2(a+y)/sina

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  17. If sin x = y sin (x + b), show that (dy)/(dx) = (sin b)/(sin^2 (x + b)...

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  18. If x^16 y^9 = (x^2 + y)^17, Prove (dy)/(dx) = (2y)/(x)

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

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