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If x ^(y) = e ^(x -y) then (dy)/(dx) =...

If `x ^(y) = e ^(x -y) ` then `(dy)/(dx) =`

A

`(1)/( (1+ log y))`

B

`(log x )/((1+ log x ) ^(2))`

C

`((log )/(1 + log x)) ^(2)`

D

`((log x ) ^(2))/( 1+ log y)`

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1B
  1. If sqrt(1- x ^(2)) + sqrt(1- y ^(2) ) = a (x -y) then (dy)/(dx)=

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  2. If y= x ^(y) then (dy)/(dx) =

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  3. If x ^(y) = e ^(x -y) then (dy)/(dx) =

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  4. If x ^(y) = log x then (dy)/(dx) at x =e is

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  5. x ^(y) =y ^(x) implies x ( x-y log x ) (dy)/(dx) =

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  6. (d)/(dx){e ^(x^(e))+ x ^(e^(x)) + e ^(x ^(x))}=

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  7. If (cos x ) ^(y) = (sin y) ^(x) then (dy)/(dx)=

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  8. If y = sqrt(x + sqrt(x + sqrt(x + .....oo)))then (dy)/(dx) =

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  9. If y = sqrt(tan x + sqrt(tan x + sqrt(tan + ....oo))) then (dy)/(dx)=

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  10. If y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ....oo))) then (dy)/(dx)

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  11. If y = x ^(x ^(x.......prop)) then (dy)/(dx)=

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  12. If y = (sin x) ^((sin x) ^((sin x) ^(...oo))), then (dy)/(dx)=

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  13. If y = e ^(x + e ^(x + e^(x ...oo))), then (dy)/(dx)=

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  14. If x = e ^(y+ e ^(y +...10oo)), x gt 0, then (dy)/(dx) is

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  15. If y = x + (1)/(x + (1)/( x +...oo)) then (dy)/(dx) =

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  16. If y = sqrtx ^(sqrtx^(sqrtx^(...oo))), then (dy)/(dx) =

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  17. If y = a ^(x ^(a^(x ^(a ^(x ...oo))))) then (dy)/(dx)=

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  18. If y = x ^(2) + (1)/(x ^(2) + (1)/( x ^(2) +...oo)), then (dy)/(dx) =

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  19. If x lt 1, then 1/(x + 1) + (2x)/(1 +x^2) + (4x^3)/(1 + x^4) + ….oo =

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  20. If lt 1 then (1-2x)/(1 - x x ^(2)) + ( 2x - 4x ^(3))/(1 - x ^(2) + x ...

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