MATH 336 Midterm: MATH 336 NIU Exam 2ans
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10/18/2002: (30 points) find these derivatives (do not simplify your answers). 3x2 + 2x + 1)8 (a) (6 pts) f (x) = (x4 f (x) = 8(x4. 6x + 2) (b) (6 pts) f (x) = (x2 + 1)3(x2 f (x) = 3(x2 + 1)2(2x)(x2 (c) (p163 #33; 6 pts) f (x) = Product rule: f (x) = (x2 (d) (p163 #37; 6pts) f (x) = 1)2 + (x2 + 1)3(2)(x2 f (x) = 1)(2x) (2x)(x2 + 1) (x2 (x2 + 1)2. 1)( 1)(x2 + 1) 2(2x) f (x) = 2x 1/2. 3 f (x) = (2x)(x2 + 1) 1 + (x2. Of course, you can use the quotient rule or product rule, as in (c), but if you can make an algebraic simpli cation it is almost always worth the time. X2 + 1 (e) (p172 #35; 6pts) f (x) = r x2 + 1. 2 (x2 + 1) 1/2(2x)(x2 f (x) = 1 f (x) =
