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f(x) = log base x^2 of (log x): find f'(e)

The same question, asked 2 times: 2 May 2023 S2, 11 May 2023 S2. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S2

    110
    If f(x)=log⁡x2(log⁡ex)f(x) = \log_{x^2}(\log_e x), then f′(x)f'(x) at x=ex = e is

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  2. Question 2

    11 May 2023 S2

    114
    If f(x)=log⁡x2(log⁡x)f(x) = \log_{x^2}(\log x), then at x=ex=e, f′(x)f'(x) has the value

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