tapered beam deflection
First and foremost, we need to verify that the beam is long enough (over 100"?) so it can be treated as a "thin" beam, instead of a true 3D structure.
For a thin beam, we would use the Euler beam equation:
where E is constant but I (the area moment of inertia) is a function of x instead. It is very difficult to solve/integrate the above nonlinear equation analytically (because I's x dependency), so some type of numerical method is required.
The wind pressure would be the distributed load term p in the above equation, and it should also be a function of x, instead of a constant. This renders the above equation even more difficult to solve, assuming you know what the distrution function is in the first place. You might want to check out the following guide from ASCE:
Wind Load Provisions
Have you considered doing this analysis emperically?