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

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

A

`3/(sqrt(1-x^2))`

B

`1/(sqrt(4-x^2))`

C

`3/(sqrt(4-x^2))`

D

`(-3)/(sqrt(1-x^2))`

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

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

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

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

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

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

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

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  8. If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=

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  9. If y = cos ^(-1) (cosx) , then (dy)/(dx) at x = (5pi)/4 is

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  10. The first derivative of the fuctioncos^(-1)(sinsqrt(1+x)/2)+x^x with ...

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  11. d/(dx){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}

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

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  13. d/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^2)))] =

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  14. If x is measured in degree , then d/(dx) (cosx) is equal to

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  15. If y = sqrt((secx-1)/(sec x +1) ) then (dy)/(dx)=

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  16. If sqrt(1- x ^(2)) + sqrt(1- y ^(2) ) = a (x -y) then (dy)/(dx)=

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  17. If f(x) = |cos x - sin x| , then f^(1)(pi/4) =

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  18. If f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x)) then (dy)/(dx) is

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  19. The value of 3 f(x ) - 2 f(1/x)=x then f^(1)(2) =

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  20. If u = f(x^2) , v = g(x^3), f^(1)(x) = sinx , g^(1)(x) = cos x then fi...

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