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Differentiate tan^(-1){(sqrt(1+x^(2))-1)...

Differentiate `tan^(-1){(sqrt(1+x^(2))-1)/(x)}` w.r.t. x.

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The correct Answer is:
`1/(2(1+x^(2)))`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(e) (LONG ANSWER TYPE QUESTIONS (I))
  1. Differentiate tan^(-1){(sqrt(1+x^(2))-1)/(x)} w.r.t. x.

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  2. tan^(-1)((sqrt(1+x^(2))+1)/(x))

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  3. Differentiate the following w.r.t. x : tan^(-1)((sqrt(1+a^(2)x^(2))-...

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  4. Differentiate the following w.r.t. x : cot^(-1)((sqrt(1+x^(2))-1)/(x...

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  5. Differentiate the following w.r.t. x : cot^(-1)((1+x)/(1-x))

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  6. Differentiate the following w.r.t. x : cot^(-1)(sqrt(1+x^(2))-x).

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  7. Differentiate the following w.r.t. x : tan^(-1)(secx+tanx).

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  8. Differentiate the following w.r.t. x : tan^(-1)sqrt((1-cosx)/(1+cosx...

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  9. Differentiate w.r.t. x: (i)tan^(-1){sqrt((1+cosx)/(1-cosx))}" "(...

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  10. Differentiate the following w.r.t. x : tan^(-1)sqrt((1+sinx)/(1-sinx...

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  11. Differentiate the following w.r.t. x : sin^(-1)(sqrt((1+x^(2))/2)).

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  12. If y=tan^(-1)((2y)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2)) , x >0 , prove t...

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  13. Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)...

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  14. Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)...

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  15. If y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sin...

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  16. (d)/(dx)[cos^(-1)sqrt(((1+x))/(2))]

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  17. If y=tan^(-1){(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))} , -...

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  18. If y="tan"^(-1)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(...

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  19. If y=sin[2t a n^(-1){sqrt((1-x)/(1+x))}],"f i n d"(dy)/(dx)

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  20. If y= tan ^(-1) ((5ax )/( a^(2) - 6x^(2))),then (dy)/(dx) =

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