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

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

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Solution:  We have ,  x^y=e^x-y

                 Taking log of    x^y=e^x-y  , we get 

                 ylog x=(x-y)log _e=(x-y)

                                      y=fracx1+log xRightarrow fracmathrmd ymathrmd x=frac(1+log x)cdot 1-xcdotfrac1x(1+log x)^2

          Hence        fracmathrmd ymathrmd x=frac(log x)(1+log x)^2.

             

                   

Posted by

Deependra Verma

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