A tensor derivative is like a number that tells you how quickly something is changing. Imagine there is a hill, and you want to find out how quickly the ground is going up or down. To do this, you measure the height of the ground at different points on the hill. You then use the numbers from all the different points to calculate how much the ground is changing as you move around the hill. This calculated number is a tensor derivative, and it tells you how quickly the ground anywhere on the hill is changing.