C2_W1_Lecture_Question about the derivative of log(x)


I am confused in this section about:

  1. how to derive to log(e^y)=y in the first screenshot below?
  2. why is d/dy(log(y)) = 1/(e^log(y)) in the second screenshot below?

Could anyone please show me how they are derived step by step? I thought about it for long time but couldn’t figure out.

Thanks a lot!

You can’t derive the relationship between logs and exponents - it’s a definition.

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This page has information on the derivatives of logs:

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Thank you so much for your prompt reply!!!