# We now have

d

dx

[x5 + y8] = 5x4 + 8y7y' =

d

dx

[9] = 0.

Rearranging this, we get

8y7y' = ??????????

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

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

1 3 2 4 6

2 1 8 5 7

3 7 2 7 9

(a) If h(x) = f(g(x)), find h'(3).

h'(3) =

(b) If

H(x) = g(f(x)), find H'(1).

H'(1) =

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Let f and g be the functions in the table below.

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

1 3 2 4 6

2 1 3 5 7

3 2 1 7 9

(a) If F(x) = f(f(x)), find F '(3).

F '(3) =

(b) If G(x) = g(g(x)), find G'(2).

G'(2) =

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If h(x) = Squareroot 4 + 3f(x), where f(3) = 4 and f '(3) = 3, find h'(3).

h'(3) =

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Write the composite function in the form

f(g(x)). [Identify the inner function

u = g(x and the outer function y = f(u).]

y = e^ 5 Squareroot x

(g(x), f(u)) =

Find the derivative dy/dx.