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If y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(...

If `y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(2)))+sin^(-1)((2ax)/(a^(2)+x^(2)))`, then `(dy)/(dx)` to

A

`a/(x^2+a^2)`

B

`(2a)/(x^2+a^2)`

C

`(4a)/(x^2+a^2) `

D

`a^2/(x^2+a^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. The derivative of sin^(-1)((2x)/(1+x^2)) with respect to cos^(-1)((1-x...

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  2. If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2)) then (dy)/(dX)=

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  3. If y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(2)))+sin^(-1)((2ax)/(a^(2)+x^(...

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  4. y = Cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] ...

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

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  6. The derivative of Sec ^(-1)"" (1)/( 2x ^(2) -1) w.r.t . sqrt(1+ 3x ) a...

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  7. If r = [ 2 phi +cos^2(2phi+pi//4)]^(1//2) , then what is the value of ...

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

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  9. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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  10. f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

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  11. If y =(logx)^(x) then (dy)/(dx) =

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  12. If x^(m) y^(n)=(x+y)^(m+n) , then dy/dx is equal to

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  13. If y = 2^(2 ^(x)), then (dy)/(dx) =

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  14. If y = (sinx)^(x) then (dy)/(dx) =

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  15. If y=x^(cosx) then (dy)/(dx)=

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  16. d/(dx){x^(tanx)} =

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  17. If y = (ax+b)^(cx+d) then (dy)/(dx) =

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  18. The derivative of y = (1-x) (2-x) (3-x) ....(n-x) at x = 1 is

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  19. If y = log {((1 +x)/(1-x )) ^(1//4) } -1/2 Tan ^(-1) (x ), then (dy)/(...

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  20. f (x) = (cos x) ( cos 2x ) …( cos nx) implies f' (x) + sum ^(n) (r tan...

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