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anonymous
 one year ago
calculate dy/dx if Ln(x+y)=e^x/y
anonymous
 one year ago
calculate dy/dx if Ln(x+y)=e^x/y

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.0this is implicit differentiation. Treat y as a function of x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you walk me through solving problem

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0give me a minute  I haven't done these for a while...

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0you 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?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0ok 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
 one year ago
Best ResponseYou've already chosen the best response.0that last line is 1 / (x + y) + y' / ( x + y)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0now 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'

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0its a bit messy first this i would do is multiply thru by y^2( x + y)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0thanks this sight is super helpful and thank you so much
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