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(d)/(dx) { log ((sqrt(x+1) -1)/(sqrt(x +...

`(d)/(dx) { log ((sqrt(x+1) -1)/(sqrt(x + 1 ) +1 )) + ( sqrtx)/(sqrt( x +1))}=`

A

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

B

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

C

`x sqrt(x +1) -2 sqrtx sqrt(x +1) (x+1)`

D

none

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

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  2. (d)/(d x ) { log (sqrt(1 +x )+ sqrt( 1 -x ))/(sqrt(1 + x ) - sqrt(1-x ...

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  3. (d)/(dx) { log ((sqrt(x+1) -1)/(sqrt(x + 1 ) +1 )) + ( sqrtx)/(sqrt( x...

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  4. (d)/(dx ) { a log ((a+ sqrt(a ^(2)- x ^(2)))/(x)) - sqrt(a ^(2) - x ^(...

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  5. (d)/(dx ) {log ((sqrt(x +a ) + sqrt(x -a ))/(sqrt(x -b) - sqrt( x -c))...

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  6. If y = log (cos x ) sin x, then , (dy)/(dx ) =

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  7. If f (x) = x-x ^(2) + x ^(3) - x ^(4) +….oo, |x| lt 1, then f '(x)=

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  8. (d)/(dx) {(x +a) (x ^(2) +a ^(2)) (x ^(4)+ a^(4)) (x ^(8) + a^(8))}=

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  9. (d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) ...

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  10. If y = (1 + x) (1 + x^(2)) .. (1 + x^(2n)), then ((dy)/(dx))(x = 0) is...

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  11. If y = log (a) x + log (x ) a + log (x ) x + log (a) a then (dy)/(dx)...

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  12. f (x) = log (e ^(x) ((x-2)/(x +2))^(3//4))impliesf'(0)=

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  13. If y =1 (1)/(1!) + (x ^(2))/(2!)+.. then (dy)/(dx)=

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  14. For |x| lt 1 if 1+ x+x ^(2) … then (dy)/(dx)=

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  15. If |x| lt 1 then (d)/(dx) (1-2x + 3x ^(2) +…)=

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  16. If |x| lt 1 then (d)/(dx) (1+2x+ 3x ^(2) +…)=

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  17. If |x| lt 1 then (d)/(dx ) [1+ (px)/(q) + (p (p+q))/(2 !)((x)/(q))^(2...

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  18. If y = exp {sin ^(2) + sin ^(4) x + sin ^(6) x +…} then (dy)/(dx)=

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  19. (d)/(dx) [x+(x ^(3))/(3 ) + (x ^(5))/(5) +...]=

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  20. (d)/(dx) {cos x ^(0)}=

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