Redo Problem 9.10, given y = f(x) = (x6 + 4)(x3 + 15). (a) Let g(x) =

Redo Problem 9.10, given y = f(x) = (x6 + 4)(x3 + 15).

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(a) Let g(x) = x6 +4 and h(x) = x3 + 15. Then g'(x) = 6x5 and h'(x) = 3x. Substituting these values in (9.3), y' = f'(x) = (x+4)(3x) + (x3 + 15)(6x5) y' = 3x8 + 12x + 6x8 + 90x5 = 9x8 + 90x5 + 12x (b) Simplifying first through multiplication, y = (x+4)(x +15)=x9 + 15x+4x +60 Then, y = 9x8 + 90x5+ 12x2 (c) The derivatives are, of course, identical.