I’m trying to check a simple calculation regarding the derivative of a matrix exponential. By hand I get $ $ \frac{d}{d\theta_1}e^{\theta_1 \mathbf{W_1}+\theta_2\mathbf{W_2}} = \mathbf{W_1}e^{\theta_1 \mathbf{W_1}+\theta_2\mathbf{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]`

?