Given that g(2)=4 and g'(2)=3, what is the value of h'(2) for the function h(x) = In(g(x))? O 4/3 O 1/4 3/4 2+3ln(2)

if you let f and g be functions that satisfy f’(2)=2 and g’(2)=-1 , may you explain to me how to find h’(2) for each function h attached below?

find g'(x) g(x) 3D 2х + 3 х - 5 Given the functions

solve it on the paper!

Find f'(x) and simplify. X X - 19 f(x) = Which of the following shows the correct application of the quotient rule? O A. O B. O C. O D. f'(x) = (x)(1)-(x-19) (1) [x - 191² (x-19)(1)-(x)(1) [x-19]² (x)(1)(x-19) (1) [x]² (x-19)(1)-(x)(1) [x]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

39.3

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

The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)

2 when a = 5 x + 1 Find (f -1)'(a) for f(x) 2x + 3 (Enter an exact answer.)