Question

Need help on a derivative question

Compute d2y/dx2 at the point (3,3)

x^2+y^2=18

Answer 1

\(\sf \color{red}{2x+2y \frac{dy}{dx}=0 \Rightarrow \frac{dy}{dx} = - \frac{x}{y}}\) now take the derivative again. Can you do that?

Answer 2

Ya so then the derivative of that is

\[\frac{ x }{ y^2\frac{ dy }{ dx } }\]

Answer 3

Correct?

Answer 4

Not quite. You can use either product rule or quotient rule.

Answer 5

Oh thats what I missed so then

\[(-1)(y^-1)+(-x)(-y^-2)\]

Answer 6

Then
\[\frac{ -1 }{ y }+\frac{ x }{ y^2 }\]

Answer 7

And then
\[\frac{ 1+x }{ y^2 }\]

Answer 8

Correct?