MATH 112 Midterm: MATH 112 UW derivsandints Solutions
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5 ln(t) + u1/2 t3/2 + c. 8t2 9t2/3 + 3t1/3 + c x2/3 + 10ex/5 + c (g) 3 (i) 12 (j) 0 (k) 1 (l) 44 (m) . 3: note: i simpli ed in a few places where it was easy to do so. You would not be expected to simplify. (a) f (x) = (b) dz dx (c) g (t) = (d) y = xex3 (e) g (t) = (x3ex + 1) 1/2(cid:2)x3ex + ex(3x2)(cid:3) 2 (y2 + 5) [1 + ln(y)] 2y2 ln(y) (y2 + 5)2. 2t + 1 (3x2) + ex3 ( 2t + 9)(e3t 4)(3) (e3t 4)(2t + 9) 1/2. 2t + 9 (f) q (r) = (ln r)3. 1 r (g) f (x) = 6(1 + 2x ln x)5(2 + 2 ln x) (h) f (t) = 3t(cid:19) x + ex ln x(cid:3) (ex ln x)(cid:0)2x x 7(cid:1)(cid:2)ex x 7(cid:1)2 (cid:0)x2 + 1 x2 4x(cid:1) [ln(x2.
