Fan Control- Will this work?

Howdy all…here’s a question for you all which I’m sure you’ve gotten before.

We have a ceiling fan with lights on it. It has a remote, for fan low, medium and high. Also it has a button for lights. Is there anyway I can control the speed of the fan? I was looking at a Ge 15Amp at lowes, but wasn’t sure if you could just control the light switch.

Update on this. I think I see they now sell a product that acts a speed control for the fan speed. Looks like a few on here have bought it and are pretty happy with it.

can you provide a link?

@LadySapphy, here you go: