What is the derivative of $c^TX^TXc$ with respect to $X$? Here, all the entries are real and $X$ is a matrix while $c$ is a vector.

I keep getting confused with the left and right multiplication. Hence, if I have these answers in both these angles, I might remember this better, based on the simple one or two line approach you would take.

The image attached below shows these results in the appendix of a book:

![enter image description here](https://i.stack.imgur.com/AblHY.png)

Let me know how we get there.