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

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

A

`(dy)/(dx)` doesn't exist at x = 1

B

`(dy)/(dx)=0` when x = 1

C

`(dy)/(dx)=(1)/(2)` when x = e

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -EXERCISE (LEVEL 1) Single Correct Answer Type Questions
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  3. If x^(y)=e^(x-y) then Find (dy)/(dx)

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  4. If f is one-one and satisfies f'(x)=sqrt(1-(f(x))^(2)) then (f^(-1))'(...

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  5. The function y=sin^(-1)x satisfies

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  6. Let f be a one-one function satisfying f'(x)=f(x) then (f^(-1))''(x) i...

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  8. If x=sin^(-1)(t^(2)-1),y=cos^(-1)(2t) then (dy)/(dx) at t = 0 is

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  9. If tan^(-1)y-y+x=0 then (d^(2)y)/(dx^(2)) is equal to

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  10. If F(x)=|{:(x,x^(2),x^(3)),(1,2x,3x^(2)),(0,2,6x):}| then F'(x) is equ...

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  11. If y=(sin^(2)x)/(1+cot x)+(cos^(2)x)/(1+tanx) then y'(x) is equal to

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  12. If z(t)=sqrt(t^(3)+1), then z'(2) is equal to

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  13. If y=cos^(-1)((4cos x-5sinx)/(sqrt(41))), then (dy)/(dx) is equal to

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  14. If y=log cos(tan^(-1)""(e^(x)-e^(-x))/(2)) then y'(0) is equal to

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  15. If the function y=log""(1)/(1+x) satisfies the relation xy'+1=f(y) the...

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  16. If y=(sin^(-1)x)/(sqrt(1-x^(2))) satisfies the relation (1-x^(2))y'-xy...

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  17. If x siny=sin(y+a) and (dy)/(dx)=(A)/(1+x^(2)-2x cos a) then the value...

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  18. If f(x)=cot^(-1)""(3x-x^(3))/(1-3x^(2)) and g(x)=sin^(-1)""^(1-x^(2))/...

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  19. Let f be a function defined for every x, such that f''=-f,f(0)=0,f'(0)...

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  20. If y=sin^(-1)(cos x) and y'(x) is identically equal to g(x) on R~{kp,k...

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