The problem involves finding the second derivative \( y'' \) in terms of \( x \) and \( y \) from the equation \( y^2 + 2y = 2x + 1 \). The context is calculus, specifically dealing with implicit differentiation.
Some participants have provided guidance on how to proceed with taking the derivative of the first derivative. There is an indication that one participant believes they have arrived at a final answer, while others have not explicitly confirmed or questioned this outcome.
The original poster and another participant both express difficulty in moving beyond the first derivative, indicating a potential gap in understanding the subsequent steps required for the second derivative.
Now, take the derivative of y'.ObviousManiac said:Homework Statement
Find y" in terms of x and y:
y^2 + 2y = 2x + 1
Homework Equations
N/A
The Attempt at a Solution
I found the first derivative:
y^2 + 2y = 2x + 1
2yy'+2y'=2
2y'.(y+1)=2
y'=2/2(y+1)
y'=1/(y+1)
But I'm having trouble moving on from there.
SammyS said:Now, take the derivative of y'.
Sure it will have y' in it, but then substitute the result you have for y' into that.