Section 14.5 Chain Rule
Exercise 56
If \(f\) is homogeneous of degree \(n\), show that \[ x^2 \frac{\partial^2 f}{\partial x^2} + 2xy \frac{\partial^2 f}{\partial x \partial y} + y^2 \frac{\partial^2 f}{\partial y^2} = n(n-1)f(x, y) \]
If \(f\) is homogeneous of degree \(n\), show that \[ x^2 \frac{\partial^2 f}{\partial x^2} + 2xy \frac{\partial^2 f}{\partial x \partial y} + y^2 \frac{\partial^2 f}{\partial y^2} = n(n-1)f(x, y) \]