Question

Find the second derivative of x^2y=3

Answer 1

\[x ^{2}*y=3\]

Answer 2

implicite?

Answer 3

Yes

Answer 4

I got 6y/x^2 by the way.
No \[\frac{ d ^{2}y }{ dx ^{2} }\]

Answer 5

Product rule

\(=(x^2)'y+x^2y'=0\\2xy+x^2y'=0\\\)
now for the second

\((2y+2xy')+2xy'+x^2y''=0\)

Answer 6

\(2y+4xy'+x^2y''=0\\y''=\frac{-2y-4xy'}{x^2}=\frac{-2y-4x(\frac{-2y}{x})}{x^2}=\frac{-2y+8y}{x^2}=\frac{6y}{x^2}\)

Answer 7

Oh Great. Thanks, that's what needed. Cheers.