Don't Understand MathWorks Model Reference Adaptive Control with Neural Network Formulation?

I've been working on creating an adaptive controller that uses a single hidden layer feedforward neural network to estimate the disturbances.

I don't understand how MathWorks uses the functions for w_dot and v_dot found here: https://www.mathworks.com/help/slcontrol/ug/model-reference-adaptive-control.html

w_dot=−(σ(VTx)−σ′(VTx)VTx)eT(t)PBΓw: Following the size of the matrices I get this: (Nx1 - Nx1 * Nx1) * 1xn * nxn * n * m.

Does it do an element wise multiplication for σ′(VTx)VTx or is σ′ a jacobian? If so wouldn't it be 1xN instead then making the dimensions not match? Or is there something else going on here that I am not understanding?

V_dot=−ΓVxeT(t)PBwTσ(VTx): Following the size of the matrices I get this: nx1 * 1xn * nxn * nxm * mxN * Nx1

For this equation did is having σ(VTx) a mistake at the end?

Following my adaptive controls book I am not sure why w_dot here is not simply just w_dot = Γσ(VTx)eT(t)PB

However my book does not have how to calculate v_dot, unfortunately. Would it not just be v_dot = ΓVxeT(t)PBwT without the σ(VTx) appended at the end?

Any help on helping me understand this would be greatly appreciated!