Vector Function Differentiation: $f(\vec x) = (\vec x - \vec y)^T(\vec x - \vec y)$

30 Views Asked by At

I am currently self-studying to learn vector calculus. Would the following be correct:

If $f(\vec x) = (\vec x - \vec y)^T(\vec x - \vec y)$, then I can rewrite it as $(\vec x - \vec y)^2$ since it is just the dot product of a vector with itself.

Which means if I want to find the derivative as follows:

$\frac{\partial f(\vec x)}{\partial \vec x} = 2(\vec x - \vec y)$

Is that correct? I simply just used the chain rule as I would do on normal scalar functions.