Find the following using the table below. 1 4 f(z) 1 4 4 1 2 3 g(z) 3 1 4 g (x 4 2 if h(x) = f(9(z)) then h'(3) =

Find h(x) if h'(x) h(x) = = 5x (6 - x²)² X and h(1) = : -6.

a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2-5x 3 find: f'(2)

Consider the following. f(x) = x³ = 6x² +8 (a) Find f'(x) and f"(x). f'(x) = F"(x) = (b) Graph f(x), f(x), and f"(x) with a graphing utility. y 150 100 50 XXX. -5 -50 -100 -150 x = -5 y 150 100 x = 50 -50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) 5 Identify x-values where F"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.) -5 y 150 100 50 -50 -100 -150 DO -5 y 150 1000 50 -50 -100 -150 X

If f(x)=(1/(x5−6x+7)^5), What is f′(x)?

If f(x)=(6/(6x2−4x−5)^3). Find f′(x

If g'(6) = 6 and h'(6) = 19, find f'(6) for f(x) = f'(6)= (Simplify your answer.) - 1 g(x) + n(x).

Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct application of the product rule? A. (0.2x+2)(0.2) + (0.6x9)(0.6) O B. (0.2x + 2)(0.6) - (0.6x-9)(0.2) O C. (0.6)(0.2) D. (0.2x + 2)(0.6) + (0.6x-9)(0.2) f'(x) =

Find f'(x) and simplify. f(x) = (0.3x + 7)(0.7x-6) Which of the following shows the correct application of the product rule? O A. (0.3x+7)(0.7) + (0.7x − 6)(0.3) B. (0.3x + 7)(0.7) - (0.7x-6)(0.3) O c. (0.3x+7)(0.3) + (0.7x-6)(0.7) O D. (0.7)(0.3) f'(x) =

Use the values in the table below to answer each of the following: f(x) g(x) f'(x) g'(x) 5 X h'(4) = 4 8 16 4 3 7 Oh'(x) -2 = (a) Let h(x) = f(x²). Find h'(x). g(x) 3 = 1 Oh'(x) = -3 0 Oh'(x) 2xg(x) f'(x²)-f(x²) g'(x) (g(x))² -1 5 6 f(x²) g'(x)−g(x) f'(x²) (g(x))² · g(x) f'(x²)-f(x²) g'(x) (g(x))² ○ h'(x) = f(x²) g'(x)—2xg(x) f'(x²) (g(x))² which tells us that h(x) is ---Select--- at x = 4 . (b) Let p(x) = g(g(x)) . Find p'(x). Op'(x) = g'(g(x)) g'(x) Op'(x) = 2g'(g(x)) p'(x) = 2g'(g(x)) g(x)+g (g(x)) g(x) p'(x) = g'(g(x)) g(x)+g (g(x)) g(x) Op'(x) = g'(g(x))