`(logx)^(x)+x^(logx)`

1.	`(logx)^(x)+x^(logx)`
Answer» `y=x^(logx)+(logx)^(x)" (माना )"` `=u+v` `rArr" "(dy)/(dx)=(du)/(dx)+(dv)/(dx)" …(1)"` अब `u=x^(logx)` `rArr" "logu=log(x^(logx))=logx.logx=(logx)^(2)` `rArr" "(1)/(u)(du)/(dx)=(2logx)/(x)` `rArr" "(du)/(dx)=(2ulogx)/(x)=(2logx)/(x).x^(logx)` और `v=(logx)^(x)` `rArr" "logv=log(logx)^(x)=xlog(logx)` `rArr" "(1)/(v)(dv)/(dx)=(x)/(xlogx)+log(logx)` `rArr" "(dv)/(x)=v[(1)/(logx)+log(logx)]` `=(logx)^(x)[(1)/(logx)+log(logx)]` समीकरण (1 ) से `(dy)/(dx)=x^(logx).(2logx)+(logx)^(x)[(1)/(logx)+log(logx)].`

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