Asked Apr 12, 2019

How would you find y' if x^y=y^x using logarithmic differentiation and keeping the answer in terms of x and y. 


Expert Answer

Step 1

Given equation:

The given equation is xy = yx.

Step 2

Find the derivative y = (dy/dx) of xy = yx:

The derivative y = (dy/dx) of xy = yx is calculated as given below:

Step 3

Further calculation:

The derivative y’ = (dy/dx) of xy = yx is obtained as (xy*lny–y2)/ (xy*lnx–x2) from the further cal...


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