Derive a rotation matrix to partial derivative

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I have the following rotation matrix:

[u = [cos θ -sin θ| [x
v] = |sin θ cos θ] y]

the rotation matrix is 2x2 (I apologize for my bad html skills)

And I need to show that the following is true:

d^2f/dx^2 + d^2f/dy^2 = d^2f/du^2 + d^2f/dv^2 (d=delta, so it's second derivative)

Any guidance will be greatly appreciated,

Cheers Tom