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If x= e^((x)/(y)), then prove that (dy)/...

If `x= e^((x)/(y))`, then prove that `(dy)/(dx)= (x-y)/(x.log x)`

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The correct Answer is:
`(x-y)/(x.log x)`
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Find (dy)/(dx) when x and y are connected by the relation given: (x...

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  2. If ax^(2) + 2hxy + by^(2) + 2gx + 2f y + c = 0, then show that (dy)/(d...

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  3. If x= e^((x)/(y)), then prove that (dy)/(dx)= (x-y)/(x.log x)

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  4. If y^(x)= e^(y-x), then prove that (dy)/(dx)= ((1+ log y)^(2))/(log y)

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  5. If y= (cos x)^((cos x)^((cos x)……oo)), then show that (dy)/(dx)= (y^(2...

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  6. If x sin (a + y) + sin a cos (a + y)= 0, then prove that (dy)/(dx)= (s...

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  7. If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= ...

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  8. If y= tan^(-1)x, then find (d^(2)y)/(dx^(2)) in terms of y alone.

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  9. Verify the Rolle's theorem for each of the function in following quest...

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  10. Verify the Rolle's theorem for each of the function in following quest...

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  11. Verify the Rolle's theorem for each of the function in following quest...

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  12. Verify the Rolle's theorem for each of the function in following quest...

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  13. Verify the Rolle's theorem for each of the function in following quest...

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  14. Discuss the applicability of Rolle's theorem on the function given by ...

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  15. Find the points on the curve y= cos x-1 in x in [0, 2pi], where the ta...

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  16. Using Rolle's theorem, find the point on the curve y= x (x-4), x in [0...

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  17. Verify mean value theorem for each of the functions: f(x) = (1)/(4x-...

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  18. Verify mean value theorem for each of the functions: f(x)= x^(3)-2x...

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  19. Verify mean value theorem for each of the functions: f(x)= sin x- s...

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  20. Verify mean value theorem for each of the functions: f(x)= sqrt(25-...

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