If `y=(cosx)^(cosx)^(cosx)^^((((oo)))),p rov et h a t(dy)/(dx)=-(y^2tanx)/((1-ylogcosx)dot`

Answer

N/a

Explanation

We have, `y = (cosx)^((cosx)^((cosx)^("....."oo)))`
`rArr y = (cosx)^(y)`
`:. log y = log(cosx)^(y)`
`rArr logy = y logcosx`
On differentiating w.r.t. we get
`1/y.(dy)/(dx)= y.(d)/(dx)log cosx+logcosx.(dy)/(dx)`
`rArr 1/y.(dy)/(dx) = (y)/(cosx).(d)/(dx) cosx+logcosx.(dy)/(dx)`
`rArr (dy)/(dx)[1/y-logcosx] = (-ysinx)/(cosx)=-ytanx`
`:. (dy)/(dx) = (-y^(2)tanx)/((1-ylogcosx))`
` = (y^(2)tanx)/(ylogcosx-1)`