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If x = e^(x//y), then dy/dx is equal to...

If `x = e^(x//y)`, then `dy/dx` is equal to

A

`(x-y)/(x log x)`

B

`(y-x)/(log x)`

C

`(y-x)/(x log x)`

D

`(x-y)/(log x)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that , ` x = e^((x)/(y))`
Taking log on both sides , we get
` log x = (x)/(y) + log e= (x)/(y) rArr x = y log x `
`rArr 1 = y .(1)/(x)+ log x. (dy)/(dx) rArr (dy)/(dx) = (x-y)/(xlog x)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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  2. If y = loga x + log xa + log x x + logaa, thendy/dx is equal to

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  3. If x = e^(x//y), then dy/dx is equal to

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  4. If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1)...

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  5. If y = t^(2) + t - 1 " then " (dy)/(dx) is equal to

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  6. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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  7. If y=sqrt(x(log)e x) , then find (dy)/(dx) at x=e .

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  8. Let y=e^(2x)dotT h e n((d^2y)/(dx^2))((d^2x)/(dy^2))i s

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  9. If f(x)=|x-2| and g(x)=f(f(x)), then g'(x)"for "x gt 20,is

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  12. If y=f(x)" and "ycosx+cosy=pi, then the value of f''(0) is

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  13. Derivatives of y = cos^(-1) sqrt((cos 3x)/(cos ^(3) x)) with respect ...

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  14. if sqrt(x^2+y^2)=ae^(tan^-1 (y/x)) , a > 0, (y(0) > 0) then y"(0) equa...

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  15. If y = In ((x)/(a + bx))^(x), "then " x^(3)(d^(y))/(dx^(2)) is equa...

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  16. If (d^(2)x)/(dy^(2)) ((dy)/(dx))^(3) + (d^(2) y)/(dx^(2)) = k , then...

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  18. If f' (x) = sin (log x) and y = f((2x+3)/(3- 2x)), " then " (dy)/(...

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  19. If u = x^(2) + y^(2) " and " x = s + 3t, y = 2s - t , " then " (d^(2...

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  20. If the function f(x) is defined by f(x) = a + bx and f^(r) = fff … ...

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