Question

Find y'' by implicit differentiation: 9x^2+y^2 = 9

Answer 1

http://www.youtube.com/watch?v=X0aw9-kXfY4

Answer 2

messed up the quotient rule...sigh

Answer 3

...

Answer 4

\[9x^2 +y^2 =9 \] \[\text{ } 18x +2y(dy/dx) = 0\] \[dy/dx=-(18x/2y)\] \[18 +2(dy/dx) + 2y(d^2y/dx^2) =0 \] \[d^2y/dx^2 = -(18 + 2(dy/dx))/2y\]
now sub in dy/dx
\[d^2y/dx^2 = -(18 - 2(18x/2y))/2y = 36(x - y)/(2y)^2\]

Answer 5

no need for the quotient rule with that method