Differentiate the following function with respect to `x :` `(log\ x)^x+x^(logx)`

Explanation

Let `y = (logx)^x+x^(logx)`

Let `u = (logx)^x and v = x^(logx)`

Then, `dy/dx = (du)/dx+(dv)/dx->(1)`

Now, `u = (logx)^x`

Taking log both sides,

`log u = xlog(logx)`

Differentiating both sides w.r.t. `x`

`1/u(du)/dx = x(1/logx)(1/x)+log(logx)`

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