Calculate the following questions:

4. (a) Simplify, and express in terms of positive indices: -3x 2 2 15 ii) 3x-2+5x3 2x-4+1 iii) 3vx5-2vx3 3 x2+x2 (b) Simplify: e 6x (e3+2x)2 e 7x+4 (c) Expand and simplify (if possible): (e4-* - (2x+1)2Derivative rules The Product Rule If y = f(x) = u(x)v(x), then dy 2= 1 dv u-+v- du dx dx dx The Quotient Rule If y = f(x) = v(x) then du dy dx 17 2 The Chain Rule If y = f(u), and u = g(x), then dx du X du dx Table of Derivatives Table of Integrals Function (y) Derivative dy Function (f(x)) |Integral ([ f(x)dx) xni+1 n + 1 + C (n # -1) sin kx kcos kx cos kx -ksin kx sin kx - cos kx + C pkx cekx In x cos kx 1 -sinkx + C ekx Tekx + C In |x| + CQuadratic formula X = -btvb2-4ac 2a Index laws am x a" = am+n (a # 0) (ab)n = anbn a" (b # 0) a = 1 (a # 0) al = a am = = (a + 0) 1 a-n = Log. laws logam + logan = loga (mn) logam - logan = loga cloga b = loga bc log a 1 = 0 10ga a = 1 In (ex) = x eln x = x Trigonometric Ratios sin 0 cos 0 tan 0 - = 30 1/2 V3 / 2 1/ V3 I =450 1 / 12 - = 60 13 / 2 1/ 2 V3 cos' 0 + sin20 = 1