Please Answer, Clear and Concise Answer. Proper Format.

Let P denote the polynomials with real coefficients on (-co, co) and let 7 denote differentiation: T(f) = f'. (Recall that P is infinite- dimensional.) Show that T : P - P is linear transformation. The transformation T(f) = f' is a linear transformation, and this can be shown based on the following properties we know about the derivative of a function. First is linearity of the derivative, and second is how we know constant coefficients behave: (f + g)' = ---Select--- v , (rf)' = Select v Additionally, we know T maps a polynomial to a polynomial, as T(f(x)) = ---Select--- v