Given the function f(x) = x4 , and suppose g(x) is some other function of x.
(a) Then the function F(x) = (g(x))^4 is the same thing as ...
a. f '(g(x)) · g'(x)
b. f(g(x))
c. f '(x)
d. f '(g(x))
e. g(f(x))
(b) By either the extended power or the chain rule, we have F '(x) =
a. g(4x^3)
b. 4 (g(x))^3 · g '(x)
c. 4 (g(x))^3
d. x^4 g'(x) + 4x^3g(x)
e. 4x^3 · g '(x)
(c) It follows that F '(2) =
a. 32(g '(x))
b. 4 · g(8) · g '(2)
c. 4 · (g(2))^3
d. g(32)
e. 4(g(2))^3 · g '(2)
Thanks ya'll!