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if y to the power x = x to the power y, prove that dy/dx=y/x(y-xlogy/x-ylogx)

if y to the power x = x to the power y, prove that dy/dx=y/x(y-xlogy/x-ylogx)


 

Grade:

4 Answers

shashank gattani
18 Points
9 years ago

take logarihtm on both sides and differenciate

firoz tharayil
4 Points
9 years ago

could u pls defferentiate it for me... i tried but couldn''t get the answer..

xyz xz
37 Points
8 years ago

taking log on both sides

 

x lny = y lnx

diff. both sides                  let dy/dx = m

then

lny + (x/y)m = (y/x) + m lnx

m= (y/x)/(y-xlogy/x-ylogx)

Yogita Bang
39 Points
8 years ago

y^x=x^y

xlogy = ylogx

(x/y)dy/dx + logy = y/x + logx(dy/dx)

dy/dx(x/y-logx) = y/x - logy

dy/dx = (y/x - logy)/(x/y-logx)

         = (y/x){1- (x/y)logy}/{x/y - logx}

         = y/x(y-xlogy/x-ylogx)

 

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