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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

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){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}

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

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

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

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

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

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

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

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

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

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  11. If sqrt(u/v)+sqrt(v/u)=6 , then (du)/(dv) =

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  12. If x = theta -(1)/(theta) , y = theta + (1)/(theta) then (dy)/(dx) =

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  13. sqrt((y)/( x))+ sqrt((x)/(y))= 2 implies (dy)/(dx) =

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  14. If f(x) = (ax + b) Cos x +(cx +d) Sin x and f^(1) (x) = x Cosx is an a...

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  15. If f(1) = 3 ,f'(1)=-1/3 , then the derivative of {x^(11) +f(x)}^(-2) a...

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  16. Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continu...

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  17. If y = f((3x+4)/(5x+6)) and f^(1)(x) = tanx^2 then (dy)/(dx) is equal...

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  18. If y =a sin x + b cos x , then y^2 + ((dy)/(dx))^2 is a

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  19. Let h(x) be differentiable for all x and let f(x) = (kx+e^(x)),h(x) wh...

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  20. d/(dx){Tan^(-1)((asinx + b cosx)/(acosx-bsinx))} =

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