How to interpret symbols ∇ Del?

Question

I have the following context

---

Let $w = [w_1, w_2]^T$

Consider $g(w) = 2w_1w_2 + w_2\cos(w_1)$

Q: Compute $\nabla_w g(w)$ and verify $\nabla_w g([\pi,1]) = [2, \pi - 1]^T$

---

I'm learning machine learning, but I don't have a lot of advanced mathematics knowledge, how to interpret the symbols $\nabla_w$ in the context?

Answer 1

Basically $\nabla_w g(w)$ is to be understood as $(\frac{\partial g}{\partial w_1}, \frac{\partial g}{\partial w_2})^T$, so you get a vector. Now, use your knowledge about how to take partial derivatives of a function of multi-variables, calculate $\nabla_w g(w)$ and evaluate the resulting expression at the prescribed point.