Question

xy+y^2=1 ; find d^2y/dx^2

Answer 1

use implicit differentiation

Answer 2

how? can you teach me..

Answer 3

@myko still there?

Answer 4

find first derivative :\(\huge y'=y+xy'+2yy'\)
or \(\huge y'=\frac{y}{1-x-2y}\)
now differentiate implicitly again:
\(\huge y''=\frac{y'(1-x-2y)-y(1-2y')}{(1-x-2y)^2}\)
now substitute \(y'=\frac{y}{1-x-2y}\) in the last expretion

Answer 5

ok?

Answer 6

oh, I noticed, there is a sign mistake in expretion that i wrote for y''. The second term in nominator should be: +y(1+2y')

Answer 7

you can check this link for more info on implicit differentiation:
http://faculty.eicc.edu/bwood/math150supnotes/supplemental11.htm

Answer 8

it's just what you need for this type of problem

Answer 9

thanks :)