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(d )/(dx ) { (2)/( sqrt(a ^(2) - b ^(2))...

`(d )/(dx ) { (2)/( sqrt(a ^(2) - b ^(2))) Tan ^(-1) (( sqrt (a -b ))/( a + b) tan (x )/(2 )) }=` `

A

` a + b sin x `

B

`a + b cos x `

C

` (1)/( a+ b sin x )`

D

`(1)/( a + b cos x )`

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1A
  1. The derivative of Cosec ^(-1) (a ^(x)) w.r.t x is

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

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

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  4. The deriavative of sqrt(Tan ^(-1)x) w.r.t x is

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  5. The derivative of sqrt(Tan ^(-1)(e ^(x))) w.r.t x is

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  6. The derivative of log (10) [Sin ^(-1) (x ^(2)) ] w.r.t x is

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  7. If y= Sin ^(-1) (x ^(2) - (1)/(2)) then (dy)/(dx) at x =0 is

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  8. (d)/(dx ) {Cos^(-1) ((a+b cos x )/(a cos x +b)) (a lt b )=

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  9. (d)/(dx) {Tan ^(-1) ((b tan x )/(a ))}=

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  10. (d)/(dx ) { Tan ^(-1) ( sqrt(|(a -b)/(a +b)|)tan ""(x)/(2))}=

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  11. {Tan ^(-1) ((a + bcos x )/( b + a cos x ))}=

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  12. (d )/(dx ) { (2)/( sqrt(a ^(2) - b ^(2))) Tan ^(-1) (( sqrt (a -b ))/(...

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  13. If y = Arc tan sqrt([(x -a)/(b -x)]) then (dy)/(dx) =

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

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  15. (d)/(dx ) { x sqrt (a ^(2) + x ^(2)) + a ^(2) Sin h ^(-1) ((x )/(a))}=

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  16. (d)/(dx ) {x sqrt (x ^(2) -a ^(2)) - a ^(2) Cosh ^(-1) ((x)/(a)) }=

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

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  18. (d)/(dx ) { (1)/( 6) log ""((x-1)^(2))/(x ^(2) + x +1 ) + (1)/( sqrt3)...

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  19. (d)/(dx ) [a Tan ^(-1) x + b log ((x-1)/(x +1)) ] = (1)/(x ^(4) - 1) i...

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  20. If y =2 Tan ^(-1) ((x sqrt2)/( 1 - x ^(2))) + log ((1+ x sqrt2 + x ^(2...

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