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

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Answer 1 · 2016-07-12T17:15:40

#dy/dx = -(e^x - y e^(xy))/(e^y - x e^(xy))#

i think you should help yourself by simplifying first

#e^x + e^y = e^(xy)#

and
#e^x + e^y - e^(xy) = 0#

then the implicit function theorem states that #dy/dx = -(f_x)/(f_y)#

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

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

#dy/dx = -(e^x - y e^(xy))/(e^y - x e^(xy))#