extended product rule the product rule can be extended to the product of three functions. (a) use the product rule twice to prove that if f, t, and h are differentiable, then s fthd9 − f9th 1 ft9h 1 fth9. (b) taking f − t − h in part (a), show that d dx f fsxdg3 − 3f fsxdg2 f9sxd (c) use part (b) to differentiate y − e 3