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Derivative of tan^-1(a + bx) at x = 0 is 1: find the relation between a and b

The same question, asked 2 times: 11 Apr 2026 S2, 15 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    11 Apr 2026 S2

    71
    If the derivative of tan⁡−1(a+bx)\tan^{-1}(a + bx) with respect to x at x=0x = 0 is 1, then a6−b3=a^6 - b^3 =

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  2. Question 2

    15 May 2026 S2

    75
    If the derivative of tan⁡−1(a+bx)\tan^{-1}(a + bx) at x=0x = 0 is 11, then 1−b3+a61 - b^3 + a^6 is:

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