View Question - What Is Dy/dx When E^xy=x+y?

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what is $${\frac{{\mathtt{dy}}}{{\mathtt{dx}}}}$$ when $${{\mathtt{e}}}^{\left({\mathtt{x}}{\mathtt{\,\times\,}}{\mathtt{y}}\right)} = {\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}$$?

Guest Mar 19, 2015
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Best Answer 

 #1avatar+130561 +10

exy = x + y

Using implicit differentiation, we have

yexy + xy'exy = 1 + y'

y' ( xexy - 1) = 1 - yexy

y' = [ 1 - yexy ] / [ xexy - 1]

CPhill Mar 19, 2015

2+0 Answers

 #1avatar+130561 +10 Best Answer

exy = x + y

Using implicit differentiation, we have

yexy + xy'exy = 1 + y'

y' ( xexy - 1) = 1 - yexy

y' = [ 1 - yexy ] / [ xexy - 1]

CPhill Mar 19, 2015 #2avatar+118725 +5

Thanks Chris,

I really need practice at these so it is great when they come onto the forum.

I even got the same answer as you - isn't that great :)

Thanks anon for giving us this question :)

Melody Mar 19, 2015 Post New Answer

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