How do you differentiate #1=e^(xy)/(e^x-ye^y)#?

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Answer 1 · 2017-04-01T19:17:10

#dy/dx= (e^x-ye^(xy))/(xe^(xy) +e^y(1+y))#

Write the equation as:

#e^x -ye^y = e^(xy)#

Differentiate both sides with respect to #x#:

#e^x - y'e^y -yy'e^y = e^(xy)(y+xy')#

Solving for #y'#:

#y'(xe^(xy) +e^y+ye^y) = e^x-ye^(xy)#

#y' = (e^x-ye^(xy))/(xe^(xy) +e^y(1+y))#