derivative question, your help will mean the world!?

Question

If a point moves on the curve x^2 + y^2 = 25, then at (0,5), d^2y / dx^2 (aka the second derivative) is what?

Answer 1

differentiate implicitly:

2x + 2yy' = 0

and then some algebra

y' = -(x/y)

then differentiate again:

y'' = (-y - (-x)*y')/y^2 = (-y + xy')/y^2

then substitute in values:

y' = -0/5 = 0

and y'' = (-5 + 0*0)/(5^2) = =-5/25 = -1/5

Answer 2

restate as y=sqrt(25-x^2)

first derivative: -sqrt(25-x^2)*x
second derivative: -sqrt(25-x^2)+sqrt(25-x^2)*x^2
at x=0, this is -5