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If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove t...

If `y=(e^x-e^(-x))/(e^x+e^(-x))` , prove that `(dy)/(dx)=1-y^2`

A

`1 + y^(2)`

B

`1-y^(2)`

C

` y^(2)-1`

D

`y^(2)-2`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Differential coefficient of log10 x w.r.t logx 10 is

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  2. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  3. If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

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  4. If y=ae^(mx)+be^(-mx) then (d^2y)/(dx^2) is

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  5. If y^(2) = ax^(2) + b , " then " (d^(2)y)/( dx^(2))

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  6. If y=(log x)/(x) then (d^(2)y)/(dx^(2))=

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  7. Differentiate the following w.r.t.x. The differentiation coneffiecient...

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  8. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

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  9. If f(x) = cos x cos 2x cos 4x cos (8x). cos 16x then find f' (pi/4)

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  10. If y = cos^(-1)(cos x) then dy/dx at x = (5pi)/4 is (i)1 (ii)-1 (ii...

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  11. If x=e^y+e^((y+ tooo)) , x >0 , then (dy)/(dx) is equal to........

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  12. if x^y . y^x =16 then dy/dx at (2,2) is equal to

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  13. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

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  14. Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 ...

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  15. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

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  16. The differential coefficient of sec^(-1)(1/(2x^2-1)) w.r.t sqrt(1-x^2)...

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  17. If t(1+x^2)=x and x^2+t^2=y then dy/dx at x=2 is

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  18. x=t cost, y=t+sin t. Then (d^2 x)/(dy^2) at t=pi/2 is

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  19. if y = sin 2x , " then " (d^(6)y)/(dx^(6)) " at" x = pi/2 is equal to

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  20. Let f(x) =|{:(x^(3), sinx,cosx),(6,-1,0),(p,p^(2),p^(3)):}| where p is...

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