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f(1) = 1, f'(1) = 3: derivative of f(f(f(x))) + (f(x))^2 at x = 1

The same question, asked 4 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S1, 20 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S2

    142
    If f(1)=1, f′(1)=3f(1)=1,\, f'(1)=3, then the derivative of f(f(f(x)))+(f(x))2f(f(f(x)))+(f(x))^2 at x=1x=1 is

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  2. Question 2

    16 May 2023 S1

    114
    If f(1)=1,f′(1)=3f(1)=1, f'(1)=3, then the derivative of f(f(f(x)))+(f(x))2f(f(f(x))) + (f(x))^2 at x=1x=1 is

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  3. Question 3

    16 May 2023 S1

    145
    If f(1)=1,f′(1)=5f(1)=1, f'(1)=5, then the derivative of f(f(f(x)))+(f(x))2f(f(f(x))) + (f(x))^2 at x=1x=1 is

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  4. Question 4

    9 May 2024 S1

    125
    If f(1)=1,f′(1)=3f(1)=1, f'(1)=3, then the derivative of f(f(f(x)))+(f(x))2f(f(f(x)))+(f(x))^2 at x=1x=1 is

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  5. Question 5

    20 Apr 2025 S1

    142
    If f(1)=1,f′(1)=3f(1) = 1,f^{'}(1) = 3, then the derivative of f(f(f(x)))+(f(x))2f(f(f(x))) + (f(x))^{2} at x=1x= 1 is

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