# Finding the second order partial derivative of an arbitrary function.

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

• 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 $y$? – Hans Lundmark Nov 28 '18 at 21:00
• Hi, yes that's correct – Andrew1024 Nov 28 '18 at 21:12