Welcome to the community. Do you notice the problem happening when you aren't typing? If you lay your hands to either side of the touchpad on the palm rest will the cursor move on its own?
The touchpad can be very sensitive and you don’t have to touch it to get it to move the cursor. The sensitivity of the touchpad can be adjusted in the touchpad drivers and you may have options to disable the touchpad completely while tapping. You can access the driver either by clicking on the touchpad icon on the taskbar if one is present or by going to control panel and then mouse.
If you did check the mouse drivers and there is no option to adjust the touchpad you may need to reinstall the touchpad drivers. They may be found from the following link.
Before installing I suggest uninstalling any existing touchpad and mouse drivers from the system. Just click on start, control panel, programs and features and look for any touchpad drivers and mouse drivers and remove them. Then download and install the driver.
Once you have the drivers installed take a look again and see if you have the option to change the sensitivity of the touchpad and if there is an option to disable the cursor while typing.
Specialize in Laptops, Mobile Devices#IWork4Dell