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Let f(x) =x^n,n si being a positive inte...

Let f(x) `=x^n,n` si being a positive integer . The value of n for which `f^(1)(a+b) =f'^(1)(a)+f^(1)(b)` when `a , b gt 0` is

A

1

B

2

C

3

D

4

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The correct Answer is:
B
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. (d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If y = sin^(-1)((sqrtx-1)/(sqrtx+1))+sec^(-1)((sqrtx+1)/(sqrtx-1)), x ...

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  16. d/(dx)(sinh^(-1)(sqrtx)) =

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  17. If y = Tan^(-1)((cosx)/(1+sinx)) then (dy)/(dx)=

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  18. d/(dx){Tan^(-1)""(x)/(1+x^2)+Tan^(-1)""(1+x^2)/x} =

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

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  20. y = sin^(-1)2x+Tan^(-1)3x + Cos^(-1)2x+Cot^(-1)3x then (dy)/(dx)

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