differentiate `(tanx)^cotx+(cotx)^(tanx)`

Explanation

Given that,
`y=(tanx)^cotx+(cotx)^(tanx)`
`=>y=e^(log(tanx)cotx)+e^(log(cotx)tanx)`
`=>y=e^(cotx log(tanx))+e^(tanx log(cotx))`
`=>(dy)/(dx)=e^(cotx log(tanx))[cotx *sec^2x/tanx - cosec^2x *log (tanx)]+e^(tanx log(cotx))[tanx*-cosec^2x/cotx +sec^2x*log(cotx)]`
`=>(dy)/(dx)=(tanx)^cotx(cosec^2x-cosec^2x*log(tanx))+(cotx)^tanx(-sec^2x+sec^2x*log(cotx))`