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Find dy/dx if y = ( cos x)^((cosx)^((co...

Find `dy/dx` if ` y = ( cos x)^((cosx)^((cosx)^((cosx)........oo`

Text Solution

Verified by Experts

`y=cosx^y`
`logy=y*logcosx`
`1/y*y'=y'logcosx+y*1/cosx-sinx`
`(y')/y-y'(logcosx)=-ytanx`
`y'(1-ylogcosx)=-y^2tanx`
`y'=((-y^2tanx)/(1-ylogcosx))`.
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