Product, quotient and chain rules

Product, quotient and chain rules Quiz

Spec 7.4 · Edexcel A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Differentiate x2sin⁡xx^{2}\sin x.

    • A. 2xcos⁡x2x\cos x
    • B. x2cos⁡x−2xsin⁡xx^{2}\cos x-2x\sin x
    • C. 2xsin⁡x+x2cos⁡x2x\sin x+x^{2}\cos x
    • D. 2xsin⁡x−x2cos⁡x2x\sin x-x^{2}\cos x

  2. 2. Differentiate cos⁡2x\cos^{2}x.

    • A. −2sin⁡xcos⁡x-2\sin x\cos x
    • B. −sin⁡2x-\sin^{2}x
    • C. 2cos⁡x2\cos x
    • D. −2cos⁡x-2\cos x

  3. 3. Differentiate sec⁡x\sec x.

    • A. cosec⁡xcot⁡x\operatorname{cosec}x\cot x
    • B. sec⁡2x\sec^{2}x
    • C. −sec⁡xtan⁡x-\sec x\tan x
    • D. sec⁡xtan⁡x\sec x\tan x

  4. 4. The radius of a circle increases at 0.50.5 cm s−1^{-1}. How fast is the area A=πr2A=\pi r^{2} changing when r=4r=4 cm?

    • A. 2π2\pi cm2^2 s−1^{-1}
    • B. 4π4\pi cm2^2 s−1^{-1}
    • C. 8π8\pi cm2^2 s−1^{-1}
    • D. 16π16\pi cm2^2 s−1^{-1}

  5. 5. Differentiate tan⁡22x\tan^{2}2x.

    • A. 2tan⁡2x2\tan2x
    • B. 2sec⁡22x2\sec^{2}2x
    • C. 4tan⁡2xsec⁡22x4\tan2x\sec^{2}2x
    • D. tan⁡2xsec⁡22x\tan2x\sec^{2}2x

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