I’m trying to check a simple calculation regarding the derivative of a matrix exponential. By hand I get

$$frac{d}{dtheta_1}e^{theta_1 mathbf{W_1}+theta_2mathbf{W_2}} = mathbf{W_1}e^{theta_1 mathbf{W_1}+theta_2mathbf{W_2}}.

$$

Checking this with Mathematica, I have

```
Assuming ({(Theta)1 (Element) Reals, {W1, W2} (Element)
Matrices({d, d}, Reals, Symmetric)},
D(MatrixExp( ((Theta)1 W1 + (Theta)2 W2)), (Theta)1))
```

which returns

```
(* W1 Derivative(1)(MatrixExp)(W1 (Theta)1 + W2 (Theta)2) *)
```

Why is there a derivatie here? And what’s the `(1)`

?