MATH 211 Midterm: MATH 211 NIU s03Test3Solution
Document Summary
Exam iii: (6 pts each) find the derivative of each of these functions. (a) f (x) = e x + xe 2x + x3. Use the formula d dx eu(x) = eu(x) u (x). 4/23/03 (4. 1 #29) f (x) = e x ( 1) +(cid:2)1 e 2x + x (e 2x ( 2))(cid:3) + 3x2. Use the product rule on the middle term. (b) f (x) = ln(5x2 7) Use the formula d dx ln(u(x)) = u (x) u(x) . (4. 2 #51) f (x) = 5x2 7 (c) f (x) = ln(cid:16)x +p1 + x2(cid:17) = ln(cid:16)x + (1 + x2)1/2(cid:17) f (x) = 1 + (1/2)(1 + x2) 1/2(2x) x + (1 + x2)1/2. Note: you can"t simplify ln(m + n ). (4. 2 #89) (d) f (x) = e. + e(1/2)x f (x) = ex1/2 (e) f (x) = ln(cid:20) D dx (x 1/2) + e(1/2)x d x5 (x + 5)2(cid:21) (algebra) dx (1/2)x = ex1/2.
