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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

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

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

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

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  4. (d)/(dx) {Sec ^(-1) ""(1)/( 1- 2x ^(2))}=

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

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  6. (d)/(dx) {Tan ^(-1) ((x-a)/(1 + ax ))}=

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

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  8. Tan^(-1)((3x-x^(3))/(1-3x^(2)))=

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

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  10. (d)/(dx) {Tan ^(-1) "" sqrt([(x)/(1-x)])}=

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

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

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

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

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

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

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

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

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

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

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