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(dy)/(dx)=e^(x-y)+e^(2log x-y)...

(dy)/(dx)=e^(x-y)+e^(2log x-y)

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If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

If e^(y)=y^(x), prove that (dy)/(dx)=((log y)^(2))/(log y-1)

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x^(y)=e^(x-y) so,prove that (dy)/(dx)=(log x)/((1+log x)^(2))

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"If "x^(y)=e^(x-y)," prove that "(dy)/(dx)=(log x)/((1+log x)^(2)).

Find (dy)/(dx) : x= e^(cos 2t) and y= e^(sin 2t) show that, (dy)/(dx)= (-y log x)/(x log y)