Use chain rule and verify the following facts:
For Euclidean vector norm $\| \cdot \| : \mathbb{R^{n}} \to \mathbb{R}$:
$$
\frac{d \| \cdot \|}{d \mathbf{x}} = \frac{\mathbf{x}}{\|x\|} ;
$$
For $f:\mathbb{R}\to \mathbb{R}$, $f(t) := t^2$ the derivative is:
$$
\frac{d f(t) }{dt} =
\frac{d t^2 }{dt} = 2t;
$$
For $g:\mathbb{R^n}\to \mathbb{R^n}$, $~g(\mathbf{x}) := \mathbf{W}\mathbf{x}$:
$$
\frac{d g(\mathbf{x}) }{d\mathbf{x}} =
\frac{d \mathbf{W}\mathbf{x} }{d\mathbf{x}} = \mathbf{W};
$$
For $h:\mathbb{R^{n\times n}}\to \mathbb{R^n}$, $~h(\mathbf{W}) := \mathbf{W}\mathbf{x}$:
$$
\frac{d h(\mathbf{W}) }{d\mathbf{W}} =
\frac{d \mathbf{W}\mathbf{x} }{d\mathbf{W}} = \mathbf{x}^\top.
$$