SOLUTION: find dy/dx if e^(x/Y) + (x/y)=2.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find dy/dx if e^(x/Y) + (x/y)=2.      Log On


   

Question 1061236: find dy/dx if e^(x/Y) + (x/y)=2.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!



Let x%2Fy%22%22=%22%22z



Then 

e%5Ez%2Aexpr%28dz%2Fdx%29%2B+dz%2Fdz%22%22=%22%220


expr%28dz%2Fdx%29%28e%5Ez%2B1%29%22%22=%22%220

Since e%5Ez%2B1%3C%3E0

dz%2Fdx%22%22=%22%220

Since z%22%22=%22%22x%2Fy

dz%2Fdx%22%22=%22%22%28y%2A1-x%2Aexpr%28dy%2Fdx%29%29%2Fy%5E2

So since dz%2Fdx%22%22=%22%220

%28y-x%2Aexpr%28dy%2Fdx%29%29%2Fy%5E2%22%22=%22%220

Multiply both sides by y²:

y-x%2Aexpr%28dy%2Fdx%29%22%22=%22%220

-x%2Aexpr%28dy%2Fdx%29%22%22=%22%22-y

dy%2Fdx%22%22=%22%22%28-y%29%2F%28-x%29

dy%2Fdx%22%22=%22%22y%2Fx

Edwin