For F(x) = Log(x) (this is log base 10), estimate F prime of (1) by
finding the average rate of change over subsequently smaller intervals
around x = 1. Find F prime(x). Does this agree with your estimation?

I need the answer written up for each step, thank you.

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Well that's interesting, this isn't a homework problem. It's from a
quiz I took and failed. I need a detailed explantion of what I did
wrong. I'm willing to walk through it, if needed.