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Worked example: Chain rule with table

Through a worked example, we explore the Chain rule with a table. Using specific x-values for functions f and g, and their derivatives, we collaboratively evaluate the derivative of a composite function F(x) = f(g(x)). By applying the chain rule, we illuminate the process, making it easy to understand.

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• is there anybody who can prove this chain rule?
• Answer is 40, cuz f'(-2)=5 ... isnt?
• No, we are trying to use the Chain Rule here.
d/dx f(g(x)) = f'(g(x))g'(x)
when x = 4, g(4) = -2
when x = -2, f'(-2) = 1
when x = 4, g'(4) = 8
1 * 8 = 8
QED
• What does f-prime and g-prime mean?
(1 vote)
• f', read as ef-prime, is the derivative of the function f. Likewise for g.
• Given the chart, how would you know which part (top or bottom) applies to f and g?
• It is explained in the video. You may need to watch it again.
• I need a proof for this magical rule
• Why do you have to multiply by g(x) in the chain rule?
Why is it not just f'(g'(x))?
• Are you aware of Leibnitz notation?(You know, the d/dx thing)

An intuition of the chain rule is that for an f(g(x)),
df/dx =df/dg * dg/dx.
If you look at this carefully, this is the chain rule.