Question

How do you determine `(d^2y)/(dx^2)` given `x-y=(x+y)^2`?

Answer 1

`y''=-8/(1+2x+2y)^3`

Explanation:

By the chain rule we get

`1-2(x+y)=y'+2y'(x+y)`
so
`y'=(1-2(x+y))/(1+2(x+y))`

`y''=(-2(1+y')(1+2(x+y))-(1-2(x+y))2(1+y'))/(1+2x+2y)^2`
pluggin the term above in the second derivative we get

`y''=-8/(1+2x+2y)^3`