Differentiate `y=(tan x)^(logx)`

Explanation

`y=(tanx)^logx`

taking log both side

`logy=logxlogtanx`

Diff. both side with respect to x

`1/ydy/dx=1/xlogtanx+logx*1/tanx*secx`

`dy/dx=y[(logtanx)/x+(logxsec^2x)/tanx]`

`dy/dx=(tanx)^logx[(logtanx)/x+(logxsec^2x)/tanx]`.