Let T be the linear operator on P1(R) defined by T(p(x))= p'(x), the derivative of p(x). Let B = {1,x} and B' = {1+x, 1-x}.Use the following theorem and the fact that:
( 1 1 )⁻¹ = ( 1/2 1/2 )
( 1 -1 ) ( 1/2 -1/2 )
to find [T]β'

Theorem:

Let T be a linear operator on a finite-dimensional vector space V,and let B and B' be ordered bases for V. Suppose that Q is thechange of coordinate matrix that changes B' coordinates into Bcoordinates. Then [T]B' =Q⁻¹[T]BQ