Define T: P3-->P3 by T(f)(t)=2f(t)+(1-t)f'(t)

Show that T is a linear transformation.

I've included the problem that I'm working on. I'm having a hard time proving this transformation is linear because of the (1-t)f'(t) term at the end of it. I'm not entirely sure what to do with it when I evaluate T(s+t)=T(s)+T(t). Do I make it (1-t+s)f'(t)?

Also looking ahead, I'm not sure how to approach part b) as he skipped that in lecture.