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

`tan^(-1)((e^(2x)+1)/(e^(2x)-1))`

A

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

B

`-(2e^(2x))/(1+e^(4x))`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
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TARGET PUBLICATION-DIFFERENTIATION -DERIVATIVE OF INVERSE FUNCTIONS
  1. Find (dy)/(dx) if y=tan^(-1)(4x)/(1+5x^2)+tan^(-1)(2+3x)/(3-2x)

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  2. Find (dy)/(dx) if y=tan^(-1)(4x)/(1+5x^2)+tan^(-1)(2+3x)/(3-2x)

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  3. d/(dx)(tan^(-1) ((cos x)/(1+sinx))=

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  4. If y = tan^(-1) (sec x - tan x ) , "then" (dy)/(dx) is equal to

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

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  6. If coty=(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt1-sinx)," then "...

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  7. If y= sin ^(-1) ((4cos x +5sin x )/( sqrt(41))) ,then (dy)/(dx)=

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  8. If y=tan^(-1) ((1+x)/(1-x)) then (dy)/(dx)=

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  9. d/(dx)(tan^(- 1)(2/(x^(- 1)-x))) is equal to

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  10. d/dx(tan^-1(x/sqrt(a^2-x^2))

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  11. d/dx(tan^-1(x/sqrt(a^2-x^2))

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  12. If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),-<x<1, Prove tha...

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  13. (d)/(dx)[sin^(-1)sqrt(((1-x))/(2)]=

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  14. tan^(-1)((e^(2x)+1)/(e^(2x)-1))

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  15. d/(dx)[sin^(- 1)((sqrt(1+x)+sqrt(1-x))/2)]=

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  16. The differential coefficient of tan^(- 1)((sqrt(1+x)-sqrt(1-x))/(sqrt...

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  17. (d)/(dx)[sin^(2)cot^(-1)( sqrt((1-x)/(1+x)))] is equal to -

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  18. If f(x)=cot^(-1)sqrt(cos2x)," then: "f'((pi)/(6))=

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  19. If f(x) = tan^(-1)(sqrt((1+sinx)/(1-sinx))), 0 lt x lt pi/2, then f'(p...

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  20. If f(x)=cos^(-1)[(1-(logx)^2)/(1+(logx)^2)] , then the value of f'(e) ...

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