Differentiate each of the following functions, using the product rule.

Note: The choice of problems is purposely kept simple in this and other sections of the book to enable students to see how various rules work. While proper and often easier to simplify a function algebraically before taking the derivative, applying the rules to the problems as given will in the long run help the student to master the rales more efficiently.

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(a) y=7x4 (4x - 10) (b) f(x) = (4x + 1)(6x5) dy dx dy dx df dx df dx (c) y = (5x+6)(2x5 - 8) == = = 7x4 (8x) + (4x210) (28x) 56x5 +112x5-280x3 = 168x5-280x (4x3 + 1)(30x4)+6x (12x) 120x7+ 30x4+72x7 = 192x7 + 30x4 y = (5x+6)(10x4) + (2x5 - 8) (20x) y' = 50x8 +60x4 + 40x8 - 160x = 90x8 + 60x4 - 160x (d) f(x) = (4-6x5) (3 + 2x8) f' = (4-6x5) (16x7) + (3+2x8) (-30x4) f' = 64x7 - 96x12 - 90x460x12 = -156x12 + 64x7 - 90x4