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(d)/(dx) {Tan ^(-1) (( x-x^(1//2 ))/(1 +...

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1B
  1. (d)/(dx) {Tan ^(-1)((x)/(1 + sqrt (1- x ^(2))))}=

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

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

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  4. (d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^...

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  5. The derivative of Tan ^(-1) "" (2x)/(1 - x ^(2)) w.r.t Cos ^(-1)"" (1-...

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  6. The derivative of Arc tan "" (2x )/( 1- x ^(2)) w.r.t. Arc sin "" (2x)...

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  7. The derivative of Tan ^(-1) "" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-...

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  8. The derivative of Cos ^(-1) "" (1- x ^(2))/( 1 + x ^(2)) w.r.t. Tan ^(...

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  9. The derivative of Sin ^(-1) "" ( 2x )/( 1 + x ^(2)) w.r.t Tan ^(-1) ...

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  10. The derivative of Cos ^(-1) (2x ^(2) -1) w.r.t. Cos ^(-1) x is

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

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  12. The derivative of Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1...

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  13. The derivative of Sin ^(-1) (3x -4x^(3)) w.r.t. Tan ^(-1)"" (x )/( sqr...

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  14. If y = sqrt(sin x + y ) then (dy)/(dx) =

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  15. If y = sqrt( cos x + y) thnd (dy)/(dx) =

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  16. If sin y = x sin (alpha + y) then (dy)/(dx) =

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  17. If cos y =x cos (a + y) then (dy)/(dx)=

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  18. If Cos ^(-1) (( x ^(2) - y ^(2))/(x ^(2) + y ^(2)))=k (a constnat), th...

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

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

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