What does this look like? The context is the following: $f(\mathbf x)$ is a function defined on the unit hypersphere $S^{n-1} = \{ \mathbf x\in\mathbb R^n : |\mathbf x| = 1 \}$ where $|\cdot|$ is the Euclidean norm. $D_{\mathbf x}^j$ is defined as a "$j^{th}$-order tangential differential operator on $S^{n-1}$ with smooth coefficients".
I understand this generalizes the concept of differential to the hypersphere, but say $f(x,y) = \sqrt{x^4 + y^4}$, how do I calculate $D_{\mathbf x}^j f$ ?
Thanks, p.