What is the derivative of x^T e^-A x w.r.t. A?

Question

What is the derivative

1. $\frac{\partial}{\partial A} x^T e^{-A} x$
2. $\frac{\partial}{\partial A} x^T e^{A} x$

To be clear, $x \in \mathbb{R}^n$, $A \in \mathbb{R}^{n \times n}$ and $e^A = \sum_{n=0}^{\infty} \frac{1}{n!} A^n$ (matrix exponential). Thanks!