take derivative of a function where the variable is a vector

Question

Suppose $f(x) = || x - b||^2$ where $x,b \in \mathbb{R}^n$, what is the expression of $f'(x)$?

Thank you!

Answer 1

1. It would be the gradient $\nabla f$, not derivative $f^\prime$.
2. For the second norm the gradient looks as follows $$\nabla f = 2(x - b)\in \mathbb{R}^n$$