I need to find the higher order partial derivative of a function. (Need to find: $\frac{\delta ^2 f}{\delta u^2}$ and $\frac{\delta ^2 f}{\delta v^2}$)

The problem is that the function is not specified only given as a function of x and y. $f(x,y)$

It's also been given that $x=Au + Bv$ and that $y=Cu + Dv$ (Kindly note that the uppercase letters are constants not variables)

I have managed to get till the first partial derivatives. I.e. $\frac{(\delta f)}{(\delta u)}$ and $\frac{(\delta f)}{(\delta v)}$

Unfortunately getting to the second derivative is where I'm completely stumped, all the solutions I found online aren't applicable as they require that the function isn't arbitrary.

Any help would be super appreciated

  • $\begingroup$ If I understand the question correctly, what you want is $\partial^2 f/\partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$? $\endgroup$ – Hans Lundmark Nov 28 '18 at 21:00
  • $\begingroup$ Hi, yes that's correct $\endgroup$ – Andrew1024 Nov 28 '18 at 21:12

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