Hi there. Well, I wanted to know how to find the second derivatives of a function using implicit differentiation. Is it possible? I think it is. I think I must use the chain rule somehow, but I don't know how... I'm in multivariable calculus since the function I'm gonna use could be seen as a function of only one variable.(adsbygoogle = window.adsbygoogle || []).push({});

An ellipse: [tex]F(x,y)=4x^2+y^2-25=0[/tex]

So we have the partial derivatives:

[tex]F_x=8x[/tex], [tex]F_y=2y[/tex]

[tex]F_{xx}=8[/tex], [tex]F_{yy}=2[/tex]

So then, using implicit differentiation:

[tex]\frac{{\partial x}}{{\partial y}}=-\displaystyle\frac{\frac{{\partial F}}{{\partial y}}}{\frac{{\partial F}}{{\partial x}}}=\displaystyle\frac{-y}{4x}[/tex]

But now if I wanna find [tex]\frac{{\partial^2 x}}{{\partial y^2}}[/tex] how should I proceed?

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# Second derivatives using implicit differentiation

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