A table of values for f, g, f ‘, and g’ is given.?

x f(x) g(x) f ‘(x) g'(x)

Answer 1

(a) h'(x) = f'(g(x))*g'(x)
.. h'(3) = f'(g(3))*g'(3) = f'(2)*9 = 5*9 = 45

(b) h'(1) = g'(f(1))*f'(1) = g'(3)*4 = 9*4 = 36

Answer 2

h(x) = f(g(x))
h'(x) = f'(g(x)) * g'(x)
h'(3) = f'(g(3)) * g'(3) = f'(2) * 9 = 5*9 = 45

H(x) = g(f(x))
H'(x) = g'(f(x)) * f'(x)
H'(1) = g'(f(1)) * f'(1) = g'(3) * 4 = 9*4 = 36

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