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If y = x^(x ^(x^(x ^(x.... oo) then prov...

If `y = x^(x ^(x^(x ^(x.... oo)` then prove that ` x dy/dx = y^2/(1- y logx )`

A

y

B

`-y`

C

`-y^(2)`

D

`y^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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TARGET PUBLICATION-DIFFERENTIATION -LOGARITHMIC DIFFERENTIATION
  1. If cos(x+y) = y sinx, then (dy)/(dx)

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  2. If sin (x+y) +cos (x+y) =1,then (dy)/(dx)=

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  3. If sin(x+y)=log(x+y) then (dy)/(dx)=

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  4. If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= -y/x (b) (3sin(x y)+4c...

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  5. If x=ysqrt(1-y^(2)), then (dy)/(dx)=

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  6. If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/...

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  7. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

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  8. If y=sqrt(sinx+y) , then (dy)/(dx) equals (cosx)/(2y-1) (b) (cosx)/(1-...

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  9. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+......oo, then prove that (dy)/(dx)...

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  10. If y=e^(x+e^(x+e^(x+..."to"oo)))," then: "(dy)/(dx)=

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  11. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo)))), then (dy)/(dx) is equal to

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  12. If y = x^(x ^(x^(x ^(x.... oo) then prove that x dy/dx = y^2/(1- y lo...

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  13. The derivative of a^(sec x ) " w.r.t."a^(tan x ) (a gt 0) is

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  14. Differentiate x=e^(theta)(theta+(1)/(theta)),y = e^(-theta)(theta-( 1)...

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  15. x=a(cos t + log tan t/2), y =a sin t

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  16. If x= a sin 2theta (1+ cos 2theta), y= b cos 2theta(1- cos 2theta), th...

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  17. If x=t log t ,y =t^(t) ,then (dy)/(dx)=

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  18. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

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  19. The derivative of sin^(-1)((2x)/(1+x^2)) w.r.t. cos^(-1)((1-x^2)/(1+x^...

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  20. The derivative of cos^(-1)((1-x^2)/(1+x^2)) w.r.t. cot^(-1)((1-3x^2)/(...

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