5.9 Differentiation rules and related rates

5.9 Differentiation rules and related rates Quiz

IB Maths: Applications and Interpretation HL: Quiz

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  1. 1. Differentiate y=sin⁡(3x)y=\sin(3x).

    • A. cos⁡3x\cos3x
    • B. −3cos⁡3x-3\cos3x
    • C. 3cos⁡3x3\cos3x
    • D. 13cos⁡3x\frac13\cos3x

  2. 2. f(x)=x3/2f(x)=x^{3/2}. Find f′(4)f'(4).

    • A. 33
    • B. 88
    • C. 66
    • D. 1.51.5

  3. 3. Differentiate y=xexy=xe^x.

    • A. exe^x
    • B. xexxe^x
    • C. ex+xe^x+x
    • D. (1+x)ex(1+x)e^x

  4. 4. Differentiate y=xx+1y=\dfrac{x}{x+1}.

    • A. 1x+1\dfrac{1}{x+1}
    • B. 1(x+1)2\dfrac{1}{(x+1)^2}
    • C. 2x+1(x+1)2\dfrac{2x+1}{(x+1)^2}
    • D. −1(x+1)2-\dfrac{1}{(x+1)^2}

  5. 5. A circle has area A=πr2A=\pi r^2. The radius increases at 0.50.5 cm s−1^{-1}. Find dAdt\frac{dA}{dt} when r=4r=4.

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

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