Problem 2.1 (Vector fields)

Question

Let $X$ be the vector field $x \partial / \partial x+y \partial / \partial y$ and $f(x, y, z)$ the function $x^2+y^2+z^2$ on $\mathbb{R}^3$. Compute $X f$.

Toğrul Topal · Accepted Answer

We have:
$$Xf = x \cdot \frac{\partial}{\partial x} f + y \cdot \frac{\partial}{\partial y} f = x \cdot 2x + y \cdot 2y = 2x^2 + 2y^2.$$

Problem 2.1 (Vector fields)

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Problem 2.1 (Vector fields)

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