Is the Boeing 777X being certified as a derivative of the 777 Classic?
Yes, Boeing applied for an amendment to the existing 777 type certificate:

On April 19, 2017 (for the Model 777-8 airplane), and May 12, 2015 (for the 777-9 airplane), Boeing applied for an amendment to Type Certificate (TC) No. T00001SE to include the new Model 777-8 and 777-9 airplanes. These airplanes are constructed with new carbon-fiber-reinforced plastic (CFRP) wings with folding wingtips.
The Model 777-9 airplane, a derivative of the Model 777-300ER airplane currently approved under TC No. T00001SE, is a stretched-fuselage, large, twin-engine airplane with seating for 408 passengers and a maximum takeoff weight of 775,000 pounds.
The Model 777-8 airplane, a shortened-body derivative of the Model 777-9 airplane, is a large, twin-engine airplane with seating for 359 passengers and a maximum takeoff weight of 775,000 pounds.

(federalregister.gov, emphasis mine)