(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Well, let's take F: [tex] x^2 y^3=0 [/tex].

Now, let's say thay y=y(x), y being an implicit function of x.

I want to find 2nd row derivative [tex] \frac{d^2y}{dx^2} [/tex]

using differential operator.

2. Relevant equations

not apply

3. The attempt at a solution

Using D for the first time:

[tex]

2xy^3dx+3x^2y^2dy=0

[/tex]

Now I can find dy/dx:

[tex]

\frac{dy}{dx}=-\frac{2xy}{3x^2}

[/tex]

pretty simple, huh?

Now, using D for the 2nd time:

[tex]

2y^3dx^2+2xy^3d^2x+12xy^2dxdy+6x^2ydy^2+3x^2y^2d^2y=0

[/tex]

Now, the question is: how to find the value of [tex] \frac{d^2y}{dx^2} [/tex] from the equation above. I know how to do it in another way, but I struggle to use that one.

Thanks in advance.

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# Homework Help: Total differential for finding higer row derivatives

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