### Chapter 3 Test #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

so, since you are trying to find the derivative of h'(1), the general equation for the h'(x) is:

then, plug in 1 for x to get:

next, look at the chart above to find g(1), g'(1), and f'(whatever g(1) equals). you get:

knowing these values, plug in those values for g(1), g'(1), and f'(whatever g(1) equals) respectively:

thus...h'(1) = -27

and theree you go.

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