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If y = x^(1/x) , the value of (dy)/(dx...

If ` y = x^(1/x)` , the value of ` (dy)/(dx)` at x =e is equal to

A

1

B

0

C

`-1`

D

`e^((1/e)-2)`

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The correct Answer is:
B
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Let f(x) =|{:(x^(3), sinx,cosx),(6,-1,0),(p,p^(2),p^(3)):}| where p is...

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  2. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

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  3. If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

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  4. If y = tan^(1-) sqrt((x+1)/(x-1)) " for " |x| gt 1 " then " (dy)/(dx)...

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  5. If y="log"(2)"log"(2)(x), then (dy)/(dx) is equal to

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  6. if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

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  7. Let the function f(x) be defined as f(x) = {:{((logx-1)/(x-e) , xnee),...

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  8. Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

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  9. Lagrange's mean value theorem is not applicable to f(x) in [1,4] where...

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  10. The value of c in Lagrange's mean value theorem for the function f(x) ...

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  11. If f be a function such that f(9)=9 and f'(9)=3, then lim(xto9)(sqrt(f...

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  12. If f(x) = {{:(1/(1+e^(1//x)), x ne 0),(0,x=0):} then f(x) is

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  13. If f(x)=sqrt(1-sqrt(1-x^2) then at x=0

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  14. Domain of differentiable of the function f(x) = |x -2| cos x is

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  15. Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the great...

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  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+ ....oo term then at x=0,f...

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  17. Let f(x)={(|x+1|)/(tan^(- 1)(x+1)), x!=-1 ,1, x!=-1 Then f(x) is

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  18. the value of lim(h to 0) (f(x+h)+f(x-h))/h is equal to

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  19. If y = (e^(x)+1)/(e^(x)-1), " then" (y^(2))/2 + (dy)/(dx) is equal to

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  20. If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

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