Thread: First and second derivative question :)

1. First and second derivative question :)

Find dy/dx and d^2y/dx^2 as functions of x and y given that xy^2+y=1.

Thank you

2. did you try doing it?

3. Attempt

I did yes.. a poor attempt.
xy^2+y=1
d/dx[xy^2+y]
y^2dy/dx+y
dy/dx=-y/y^2
dy/dx=-1/y

4. Originally Posted by lyoung
I did yes.. a poor attempt.
xy^2+y=1
d/dx[xy^2+y]
y^2dy/dx+y
dy/dx=-y/y^2
dy/dx=-1/y
You did the derivative of the first term wrong. And you never took the derivative of the last term on the LHS.
d/dx(xy^2 + y) = y^2 + 2xy*y' + y'

-Dan

5. Where does the +y' come from? Is it not a negative?

6. Originally Posted by lyoung
Where does the +y' come from? Is it not a negative?
If you multiply out the LHS side of Dan's line in post 4 before differentiating you get

d/dx(xy^2) + d/dx(y).

Now differentiate this and you will get the RHS of Dan's post 4.