Find the following using the table below.

Question

x	1	2	3	4
f(x)	1	2	3	4
f′(x)	2	4	3	1
g(x)	2	1	3	4
g′(x)	4	2	1	3

h'(3) if h(x) = f(x) g(x)

h′(3) if h(x)=f(x)/g(x)

h′(3) if h(x) = f(g(x)  

Answer 1

This problem tests your knowledge of the rules of differentiation. Now remember when you want to substitute, start with the function with x and then replace x with 3.

Product rule

h(x) = f(x) g(x) ⇒ h'(x) = f'(x) g(x) + f(x) g'(x)

Quotient rule

h(x) = f(x)/g(x) ⇒ h'(x) = [f'(x) g(x) - f(x) g'(x)]/(g(x))²

Chain rule

h(x) = f(g(x)) ⇒ h'(x) = f'(g(x)). g'(x)

Now read the values for x = 3 from the table to find the values. I will set up the last one but you can find the values for all of them

h'(3) = f'(g(3)).g'(3)= f'(3).1 since g(3) = 3 and g'(3) =1