Answer using product rule taught in grade 12 at high school level calculus

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 + 7ac) (2 - 3) b. f ( 2) = (5ac2 + 320) (203 + 220 - 1) c. h(x) = (1 -22) (1+2 2 ) d. y = 2(sin ac) (cos x) e. f(ac) = -23 Vac f. k(x) = (723 + 2) (3 sin ac) 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) (x 2 + 2x + 1 )