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If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))...

If `y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))` , prove that `(dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}`

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