(1 point) Let h(a) = tan(2"). Which of the following best describes its fundamental algebraic structure? O A. A composition f(g(x) ) of basic functions O B. A sum f(ac) + g(a) of basic functions O C. A product f(a) . g(a) of basic functions O D. A quotient f(a) / g(a) of basic functions where f(z) = g(x)(1 point) Let f and g be the functions dened by t) = 3t2 and W) = t3 + 7t. Determine f'(t) and g'{t). f'tt) = 9%) = Let pa) = 3t2{t3 + 7t) and observe that pa) 2 t) - 9(t). Rewrite the formula for p by distributing the 3t2 term. Then, compute p') using the sum and constant multiple rules. p') = True or False: p'} = f'(t} -g"{t} ? v (1 point) Find the derivative of the function g() = 14 g'(x) =(1 point) Use the Product Rule to find the derivative of f. f(x) = cot(x) cos(x) f' (a) =(1 point) The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x) = F(x) G(x) and Q(x) = F(a) / G(a). Answer the following questions. -110- 1. P (1) = 2. Q' (1) = 3. P' (6) = 4. Q' (6) =(1 point) Find the derivative of f(x) = x sin (x6) f' (z) = Find the derivative of g(x) = V3x4 - 3 g' (x) = Find the derivative of 2x + 3 h(x) = 3x2 +5 h' (a) =(1 point) Find the second derivative of f(a:) = 69': + 5606(1) sin(a:) me) = | \\ Find the derivative of 9(2) 2 tan5(2a:) +si11(89:3 53: + 1) 919:) = i ' (1 point) Suppose that 11%) = 3 and f'(';) = 4, and let 9(1) 2 at) sine: and ME] = (25?. Answer the following questions. a: 1. Find g'(ar/3). Answer: g'(1r/3) = 2. Find h'(1r/3). Answer: h'(1r/3) = (1 point) Calculate the derivative using the appropriate rule or combination of rules. 61' \" 2 (er+3)(x+3) f'(a:} = ' (3xe\"x+6e\"xe\"2x)f((e"x+3)\"2(x+3}-'2] (1 point) Let f($) = 2:11!\" 3. Answer the following questions. 1. Find the rst derivative of at). Answer: 3" (2:) = 2. Find the second derivative of an). Answer: f\"(:.-:} =