take derivative of tensor $f(\mathcal{X})= \| \mathcal{X} - \mathcal{A} \|_F^2 + \alpha\| \mathcal{X} - \mathcal{B} \|_F^2 $

Question

I have an optimization function

$$\begin{array}{ll} \text{minimize} & f(\mathcal{X})= \| \mathcal{X} - \mathcal{A} \|_F^2 + \alpha\| \mathcal{X} - \mathcal{B} \|_F^2\\ \end{array}$$

where $\mathcal{X} $, $\mathcal{A} $ and $\mathcal{B} $ are all third-order tensor. How to obtain the optimal solution $\mathcal{X} $?

Here is one of my answer:

take the derivative with respect to $\mathcal{X} $, we have

$2(\mathcal{X} - \mathcal{A}) + 2\alpha(\mathcal{X} - \mathcal{B}) =0$

then we can get

$\mathcal{X} = (\mathcal{A} + \alpha\mathcal{B} ) / (1+\alpha)$

I use the way to deal with the matrix. Is it correct? Does tensor have the derivative properties like the matrix?

Thanks

BS: the tensor here is a high dimensional matrix, and it defined like this.