### 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

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