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If f(x) = log(x)(lnx) then f'(x) at x = ...

If `f(x) = log_(x)(lnx)` then f'(x) at x = e is

A

`1//e`

B

e

C

`-1//e`

D

0

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The correct Answer is:
A
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. If f(x)=a^x/x^a then f'(a) =

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  2. If y =sqrt((1-sin2x)/(1+sin2x)) then ((dy)/(dx))(x = 0) =

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  3. If f(x) = log(x)(lnx) then f'(x) at x = e is

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  4. (d)/(dx){log(x+sqrt(a^2+x^2))} =

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  5. The derivative of y = (1-x) (2-x) ...(n-x) at x = 1 is

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  6. f (x)= (1)/(1+ (1)/(x))g (x) =(1)/(1 + (1)/(f(x)))implies g'(2)=

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  7. (d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) ...

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  8. (d)/(dx) {cos x ^(0)}=

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  9. Let f(x) =x^n,n si being a positive integer . The value of n for which...

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  10. If y = (sin^2x)/(1+cotx)+(cos^2x)/(1+tanx) then dy/dx is equal to

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  11. If y=(x+sqrt(x^2-a^2))^n then (x^2-a^2)((dy)/(dx))^2=

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  12. If f(x) = sqrt(1+cos^2(x^2)) , then f'((sqrtpi)/2) is

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  13. If f(x)=x/(sqrt(1-x^2)),g(x) = x/(sqrt(1+x^2)) , then d/(dx)(fog(x)) =

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  14. If x = a{costheta + log tan((theta)/(2))} andy = a sin theta, then (dy...

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  15. If f(x) and g(x) are two functions with g(x) = x -1/x and fog (x) = x...

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  16. If sin y + e ^(-xcos y)=e then (dy)/(dx) at (1,pi) is equal to

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  17. If y= sqrt((a-x)(x-b))-(a-b)tan^(-1)sqrt((a-x)/(x-b))(a gtb) then (dy...

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  18. If y=|cosx|+|sinx|, then (dy)/(dx) at x = (2pi)/3 is

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  19. Given that f(x) is a differentiable function of x and that f(x) ,f(y) ...

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  20. If y = Tan^(-1)(cot(pi/2-x)) then (dy)/(dx) =

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