5.6 Further differentiation rules

5.6 Further differentiation rules Quiz

IB Maths: Analysis and Approaches SL: Quiz

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5 questions, one answer each

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  1. 1. Find ddx(4x3/2)\dfrac{d}{dx}\left(4x^{3/2}\right).

    • A. 6x1/26x^{1/2}
    • B. 6x5/26x^{5/2}
    • C. 85x5/2\dfrac{8}{5}x^{5/2}
    • D. 4x1/24x^{1/2}

  2. 2. Find ddxsin⁡(5x)\dfrac{d}{dx}\sin(5x).

    • A. cos⁡(5x)\cos(5x)
    • B. −5cos⁡(5x)-5\cos(5x)
    • C. 5cos⁡(5x)5\cos(5x)
    • D. 15cos⁡(5x)\dfrac15\cos(5x)

  3. 3. Find ddx(xex)\dfrac{d}{dx}\left(xe^{x}\right).

    • A. exe^{x}
    • B. xexxe^{x}
    • C. (x+1)ex(x+1)e^{x}
    • D. (x−1)ex(x-1)e^{x}

  4. 4. Find ddxln⁡(3x2+1)\dfrac{d}{dx}\ln(3x^{2}+1).

    • A. 13x2+1\dfrac{1}{3x^{2}+1}
    • B. 6x3x2+1\dfrac{6x}{3x^{2}+1}
    • C. 6xx\dfrac{6x}{x}
    • D. 6xln⁡(3x2+1)6x\ln(3x^{2}+1)

  5. 5. Find ddx(sin⁡xx)\dfrac{d}{dx}\left(\dfrac{\sin x}{x}\right).

    • A. cos⁡x1\dfrac{\cos x}{1}
    • B. sin⁡x−xcos⁡xx2\dfrac{\sin x-x\cos x}{x^{2}}
    • C. xcos⁡x+sin⁡xx2\dfrac{x\cos x+\sin x}{x^{2}}
    • D. xcos⁡x−sin⁡xx2\dfrac{x\cos x-\sin x}{x^{2}}

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