anonymous
  • anonymous
calculate dy/dx if Ln(x+y)=e^x/y
Mathematics
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anonymous
  • anonymous
calculate dy/dx if Ln(x+y)=e^x/y
Mathematics
jamiebookeater
  • jamiebookeater
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welshfella
  • welshfella
this is implicit differentiation. Treat y as a function of x
anonymous
  • anonymous
can you walk me through solving problem
welshfella
  • welshfella
give me a minute - I haven't done these for a while...

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welshfella
  • welshfella
you differentiate term by term so first do ln(x + y) you use the chain rule here as you have a function within a function are you familiar with the chain rule?
anonymous
  • anonymous
yes
welshfella
  • welshfella
ok so derivative of ln (x + y) = 1 / (x + y) * d(x+y)/dx = 1( x + y) * ( 1 + y') = 1 (x +y) + y' / (x + y) ( I've written dy/dx as y')
welshfella
  • welshfella
that last line is 1 / (x + y) + y' / ( x + y)
anonymous
  • anonymous
ok
welshfella
  • welshfella
now find derivative of the right hand side Use the quotient rule =[ y* e^x - e^x * y'] / y^2 so we have 1 / (x + y) + y' / ( x + y) = [ e^x( y - y')] / y^2 now you need to solve for y'
anonymous
  • anonymous
ok
welshfella
  • welshfella
its a bit messy first this i would do is multiply thru by y^2( x + y)
anonymous
  • anonymous
yes this is allot
welshfella
  • welshfella
I got dy/dx = xy e^x + y^2 e^x - y^2 ------------------- y^2 + x e^x + y e^x but work it but for yourself
anonymous
  • anonymous
thanks this sight is super helpful and thank you so much
welshfella
  • welshfella
yw

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