SOLUTION: Please explain how to solve using implicit differentiation. {{{ e^(xy)=4x+4y+20 }}} Thank you

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Question 992887: Please explain how to solve using implicit differentiation.
+e%5E%28xy%29=4x%2B4y%2B20+
Thank you
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Please explain how to solve using implicit differentiation.

+e%5E%28xy%29=4x%2B4y%2B20+
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Take the differential of both sides.  Use the rule of taking the differential of a composite function and taking the differential of a product:

d%28e%5Exy%29 = 4%2Adx+%2B+4%2Ady,

%28dx%2Ay+%2B+x%2Ady%29%2A%28e%5Exy%29 = 4%2Adx+%2B+4%2Ady.

Next,  express  dy  via  dx  in the form   dy = g*dy,   where  g  is a function of  x  and  y.

Then   dy%2Fdx = g%28x%2Cy%29.