1. Find the derivative for g(x) = (x2+ 1)(3x4 - 2x3) a) by expanding first, then simplifying and finding the derivative of each term (ie. without using the Product Rule) b) by using the Product Rule Note : Both derivatives should be the same. 2. Find the derivative for each of the following functions. Simplify your final answer. a. g(x) = (2+7x)(x-3) b. f (x) = (5x2 + 3x) (x3 + 2x - 1) c. h(x) = (1-x2) (1+x2) d. y = 2(sin x)(cos x) e. f ( x) =-x3 x f. k(x) = (7x3 + x) (3 sinx) 3. Find the derivative for - m(x) = -ex cos x and then evaluate at x = 0 and at x = 1 (ie. find m'(0) and m'(1)). Make sure that your calculator MODE is set to RADIANS when evaluating the "trigonometric" part of the function. Show both a graphic (Desmos) and algebraic solution. 4. Determine the point(s) where the tangent to the curve is horizontal (the slope of the tangent line is zero (0)) for the function y = (x2+2x+1)(x2+2x+1)