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If f(x) and g(x) are two functions with...

If f(x) and g(x) are two functions with `g(x) = x -1/x and fog (x) = x^3 -x/x^3` then `f^(1)(x)=`

A

`x^2-1/x^2`

B

`x^2+1/x^2`

C

`3(x^2+1)`

D

`3x^2+3//x^4`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. If f(x)=x/(sqrt(1-x^2)),g(x) = x/(sqrt(1+x^2)) , then d/(dx)(fog(x)) =

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. d/(dx){cos^(-1)x+Sin^(-1)sqrt(1-x^2)}

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  16. (d)/(dx) {Sin ^(-1) ((3x)/(2) - (x ^(3))/(2))}=

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  17. d/(dx){cos^(-1)((4x^3)/27-x)}=

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  18. If y = Tan^(-1)((3a^2x-x^3)/(a^3-3ax^2))then (dy)/(dx)=

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  19. d/(dx)(Tan^(-1)""(x)/(sqrt(a^2-x^2))=

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  20. d/(dx)(Tan^(-1)(sinhx))=

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