Whenever I teach differentiation I find that students are able to do the process fairly easily, but understanding that differentiation tells us the gradient function and what this actually means is something that students can find difficult to grasp. Here are a few interactive ideas for developing this sense, making use of Geogebra, Desmos and Autograph.
Autograph Tangents and Slow Plot
Autograph is a fantastic tool for demonstrating the gradient function.
You can easily create a function and attach a point with a tangent to the function, and then move this point to show the gradient at a point. Alternatively you can use the slow plot feature and the gradient function tool (in Advanced mode) to dynamically create the gradient function. This handily pauses on the key points (stationary and inflection points). 
I usually get the students to draw what they think the derivative (gradient) function will look like, and then use the slow plot to reveal if they are correct. It is great to use lots of weird and wonderful functions here too!
You can also show the tangent to a given function at a point easily on Desmos, as in this template I created. Simply change the function in line 1 for it to adapt automatically. You can show the gradient function by selecting to show line 6, but it does not appear nicely like with the slow plot in Autograph.


This is a great little game (created by John Golden in Geogebra) where students have to guess the derivative of a randomly generated function at a given point. They are scored (from 0 to 100) on how accurate they are in their guess. Get students to play 10 rounds, and then submit their score to the class to compare.
For a bigger challenge, you can also have them guess the second derivative! 
This is a DESMOS Teacher Activity, and so has the fantastic power of you as a teacher being able to see their responses, and share them on the projector to discuss misconceptions.
It simply asks students to sketch the derivative for some different graphs, and later asks them to go the other way round to stretch them. 