A. find y'' by implicit differentiation A. if xy+e^y=e, find the value of y'' at the point where x=0

Question

A. find y'' by implicit differentiation 

x^2+xy+y^2=3

 

i got to xy'(y)'=2x-2y idk if that is correct but I know  there is more steps 

 

 

A. if xy+e^y=e, find the value of y'' at the point where x=0

 

idk where to start for this one. do i plug in 0 for x or so i take derivatives? 

Answer 1

A. if xy+e^y=e, find the value of y'' at the point where x=0.

 

To start, we get 1y + xy' +e^yy' = 0.  (first two terms come from diff. of product xy, implicitly).

 

Next, another stage of implicit differentiation yields y' + y' + xy" + ey(y')² + e^yy" = 0.

Check my work...if you agree, then it's time to substitute x=0 et cetera...