Question: 3. (a) Let f E D(R). Show that the distributional derivates of f satisfies f = (f'). (b) In general, show that if f E

3. (a) Let f E D(R). Show that the distributional derivates of f satisfies f" = (f'). (b) In general, show that if f E D(IRd), then go1 392 . . . 0am+l . . . 0gaf = 0x., (021023 - - - 0gm - - - 0gaf ) (c) Let Gi(t, x) = H(t) + H(t - x) where H is the Heaviside function. Denote R1 := 0.G1 + 0,G, E D'(R). Find R1. (d) (Bonus for Math 418/Required for Math 718) Let Go(t, z) = H(t)HI(t - ) where is the Heaviside function. Denote R2 := 0, G2 + 0,G2 c D'(R). Find R2

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