<s>[INST] 2nd order implicit derivative What would the 2nd order implicit derivative of $y^2=12x$ be?
I get the first derivative is $2yy'=12$ but Wolfram gives the second as $y''=\frac{-3}{xy}$ and I don't understand how they get that.
 [/INST] $$ y^2 = 12x \Rightarrow \\ 2\cdot y \frac{dy}{dx} = 12 \Rightarrow \\ \frac{dy}{dx} = \frac{12}{2y} = \frac{6}{y} \Rightarrow \\ \frac{d^2y}{dx^2} = -\frac{6}{1}\cdot  \frac{1}{y^2}\cdot \frac{dy}{dx} = -\frac{6}{1}\cdot  \frac{1}{y^2}\cdot  \frac{6}{y} = -\frac{36}{y^3} = -36\cdot \frac{1}{y^2\cdot y} = -36\cdot \frac{1}{12xy} = \frac{-3}{xy} $$ 
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