What is the derivative of y when x^y = y^x?

Can someone please give me the steps to solving this equation?

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- Oct 22nd 2009, 08:54 PMamma0913x^y = y^x
What is the derivative of y when x^y = y^x?

Can someone please give me the steps to solving this equation? - Oct 22nd 2009, 10:12 PMcalum
The first step is to take the natural log of both sides:

Taking the derivative of both sides with respect to x, using the product and chain rules, gets: