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Derivative of a sum of two tan^-1 terms written in log x

The same question, asked 2 times: 10 May 2024 S2*, 18 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    120
    If y=tan⁡−1 ⁣(log⁡(e/x2)log⁡(ex2))+tan⁡−1 ⁣(4+2log⁡x1−8log⁡x)y=\tan^{-1}\!\left(\dfrac{\log(e/x^2)}{\log(ex^2)}\right)+\tan^{-1}\!\left(\dfrac{4+2\log x}{1-8\log x}\right), then dydx\dfrac{dy}{dx} is

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  2. Question 2

    18 Apr 2026 S1

    69
    If y=tan⁡−1(log⁡(ex3)log⁡ex3)+tan⁡−1(log⁡(e4x3)log⁡(ex12)),x∈(e−13,e112)y = \tan^{-1}\left(\dfrac{\log\left(\frac{e}{x^3}\right)}{\log ex^3}\right) + \tan^{-1}\left(\dfrac{\log(e^4x^3)}{\log\left(\frac{e}{x^{12}}\right)}\right), x \in \left(e^{-\frac{1}{3}}, e^{\frac{1}{12}}\right) then dydx\dfrac{dy}{dx} is equal to...

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