Gradient of vector and scalar

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I have gotten the task of finding the gradient of f with respect to $\overline{x}$. The function is $f(\overline{x}) = \overline{x}^T\overline{x}+c$, where $\overline{x}$ is a vector and c is a scalar.

I know I have to derive it to find the gradient, and so far I have come to the derivative being $2\overline{x}$ since $\overline{x}^T\overline{x}=2\overline{x}$. The only part I am unsure about is what happens with the scalar? Is it just going to be 0, hence the gradient will just become $2\overline{x}$?

Thanks in advance.