Question

calculate dy/dx if Ln(x+y)=e^x/y

Answer 1

this is implicit differentiation. Treat y as a function of x

Answer 2

can you walk me through solving problem

Answer 3

give me a minute - I haven't done these for a while...

Answer 4

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?

Answer 5

yes

Answer 6

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')

Answer 7

that last line is
1 / (x + y) + y' / ( x + y)

Answer 8

ok

Answer 9

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'

Answer 10

ok

Answer 11

its a bit messy
first this i would do is multiply thru by y^2( x + y)

Answer 12

yes this is allot

Answer 13

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

Answer 14

thanks this sight is super helpful and thank you so much

Answer 15

yw