Expert: Ahmed Salami - 10/21/2008

Question
I need to find dy/dx  if   xey  + 1 =  xy using implicit differentiation.  Can you please help me?

Answer
Hi Casey,
I'm taking it you meant to write
xe^y + 1 =  xy
The trick to implicit differentiation is to always add dy/dx after
differentiating any expression in y. We'll be using the product rule
here.
Note that (d/dx)e^x = e^x
So,
x(e^y)dy/dx + (e^y).1  +  0 = x.1.dy/dx + y.1
x(e^y)dy/dx + (e^y) = x(dy/dx) + y
x(e^y)dy/dx - x(dy/dx) = y - e^y
x(dy/dx)(e^y - 1) = y - e^y
dy/dx = (y - e^y) / x(e^y - 1)

Regards.