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If y=e^x^e^x+e^x^x^e , prove that (dy)/(...

If `y=e^x^e^x+e^x^x^e` , prove that `(dy)/(dx)=e^x^e^xdotx^e^x{(e^x)/x+edotlogx}+x^e^e^xdote^e^x{1/x+dotlogx}+e^x^x^ex^x^ex^(e-1){1+elogx}`

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Verified by Experts

Taking log on both sides log
`y=e^{x} log e^{x}+x^{e} log e^{x}`
`=e^{x}(x)+x e(x) `
` implies x e^{x}+x^{e+1}`

...
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  19. Find (dy)/(dx) , when x=(e^t+e^(-t))/2 and y=(e^t-e^(-t))/2

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