Chapter 3 Test Question 6

A table of values for f, g, f', and g' is given.

If h(x)=f(g(x)), find h'(1).

x...f(x)...g(x)...f'(x)..g'(x)

1....-5.....3.......-2......-3

2.....4......2........1.....-10

3....10.....6........9......-9

In order to solve this, you need to use the chain rule. The chain rule states that for function h(x)=f(g(x), h'(x)=f'(g(x))(g'(x)). So if we plug in the values given into this equation, we get:

h'(1)=f'(g(1))(g'(1))

h'(1)=f'(3)(-3)

h'(1)=(9)(-3)

h'(1)=-27