Please help! How to find f'(5)? Please use the chain rule.?

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if:

f(x) = [g(x)]³

Then we can set up the chain rule:

f = u³ and u = g(x)
df/du = 3u² and du/dx = g'(x)

so:

df/dx = df/du * du/dx
df/dx = 3u² g'(x)
df/dx = 3[g(x)]² g'(x)

or:

f'(x) = 3[g(x)]² g'(x)

You are to find f'(5), so we substitute our values for x:

f'(5) = 3[g(5)]² g'(5)

We know what g(5) and g'(5) are so we can substitute those:

f'(-5) = 3(-3)² * 6

And simplify:

f'(-5) = 18(9)
f'(-5) = 162...Show more