PYQ Vault
EbooksTutor

Derivative of tan^-1((a + bx)/(b - ax)) + tan^-1(cx/(1 + dx^2)) by splitting into differences

The same question, asked 3 times: 3 May 2023 S2*, 16 May 2023 S2, 25 Apr 2025 S1. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    3 May 2023 S2

    141
    If y=tan⁡−1 ⁣(3+2x2−3x)+tan⁡−1 ⁣(3x1+4x2)y=\tan^{-1}\!\left(\frac{3+2x}{2-3x}\right)+\tan^{-1}\!\left(\frac{3x}{1+4x^{2}}\right), then dydx\frac{dy}{dx} is equal to

    Tap an option to check your answer.

  2. Question 2

    16 May 2023 S2

    119
    If y=tan⁡−12+3x3−2x+tan⁡−14x1+5x2y = \tan^{-1}\frac{2+3x}{3-2x} + \tan^{-1}\frac{4x}{1+5x^2}, then dydx=\frac{dy}{dx} =

    Tap an option to check your answer.

  3. Question 3

    25 Apr 2025 S1

    112
    If y=tan⁡−1(4x1+5x2)+cot⁡−1(3−2x2+3x)y=\tan^{- 1}\left( \frac{4x}{1 + 5x^{2}} \right)+\cot^{- 1}\left( \frac{3 - 2x}{2 + 3x} \right), then dydx\frac{dy}{dx} is equal to

    Tap an option to check your answer.