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I'm trying to find $y''$ by implicit differentiation of this problem: $4x^2 + y^2 = 3$

So far, I was able to get $y'$ which is $\frac{-4x}{y}$

How do I go about getting $y''$? I am kind of lost on that part.

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up vote 3 down vote accepted

You have $$y'=-\frac{4x}y\;.$$ Differentiate both sides with respect to $x$:


Finally, substitute the known value of $y'$:


But from the original equation we know that $4x^2+y^2=3$, so in the end we have


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Shouldnt the answer be $\frac{-12}{y^3}$ – soniccool Jun 29 '12 at 20:49
Since $4x^2+y^2$ since x and y must satisfy the original equation – soniccool Jun 29 '12 at 20:56
@soniccool: Yes: I inadvertently dropped a factor of $4$ in one term near the end. It’s fixed now. – Brian M. Scott Jun 29 '12 at 21:00
Yes i was right!! Im learning! – soniccool Jun 29 '12 at 21:01

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