how do you do this? they both employ the same rules and I get confused along the

Question

how do you do this? they both employ the same rules and I get confused along the way. thanks in advance!

If F(x) = f(g(x)), where f(0) = 7, f'(0) = 9, f'(-4) = 4, g(-4) = 4, find F'(-4). F'(-4) = 0 Please try again using the Chain rule to find the derivative of F(x). All the necessary values you need to evaluate F'(x) at the given point are provided in the statement of the problem. Keep in mind that d/dxf(g(x)) = f'(g(x)).g'(x). Let f and g be the functions in the table below. If F(x) = f(f(x)), find F'(3). F'(3) = If G(x) = g(g(x)), find G'(1). G'(1) =

Explanation / Answer

F'(x) = f ' ( g(x) ) * g'(x)

F' ( -4) = f'( g(-4) ) * g'(-4)

= f' ( 0) * 4

= 9 * 4

= 36

a) F(x) = f( f(x)

F' (x) = f' ( f(x) ) f' (x)

F' ( 3) = f' ( 2) * 7

= 5*7

= 35

b) G(x) = g( g(x)

G' (x) = g ' ( g(x) ) g ' (x)

G'(1) = g' ( 2) * 6

= 7 * 6

= 42

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