7. If F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6.. Find F'(5)
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I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

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

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

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

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

by jannat <33

Step-by-step explanation:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

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

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

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

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

47

step-by-step explanation: