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If y=(cos x)^((cosx)^cosx...infty), then...

If `y=(cos x)^((cosx)^cosx...infty)`, then dy/dx is equal to

A

`(ytanx)/(ylogcosx-1)`

B

`(y^2tanx)/(ylogcosx-1)`

C

`(ytanx)/(1+ylogcosx)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If y = (cos x)^((cosx)^((cos x)...oo)), " then " dy/dx is equal to

    A
    `(y tan x)/(y log cos x-1)`
    B
    `(y^(2) tan x)/(y log cos x-1)`
    C
    `(y tan x)/(1+y log cos x)`
    D
    None of these

  • If y=(cosx)^((cosx)) then (dy)/(dx) is equal to :

    A
    `(-y^(2)tanx)/(1-yln(cosx))`
    B
    `(y^(2)tanx)/(1+yln(cosx))`
    C
    `(y^(2)tanx)/(1-yln(sinx))`
    D
    `(y^(2)sinx)/(1-yln(sinx))`

  • If y=log_(sinx)cosx , then dy/dx is equal to

    A
    `(tanxlog(sinx)-cotxlogcosx)/((logsinx)^2)`
    B
    `(-tanxlogsinx-cotxlogcosx)/((logsinx)^2)`
    C
    `(-tanxlog(sinx)-cotxlogcosx)/((logsinx)^2)`
    D
    `(tanxlog(sinx)-cotxlog(cosx))/([(logsinx)^2])

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