Differentiating exponentials, logarithms and trigonometric functions

Differentiating exponentials, logarithms and trigonometric functions Quiz

Spec G2 · AQA A-Level Maths: Quiz

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  1. 1. Differentiate y=5e2x+ln⁡xy=5e^{2x}+\ln x.

    • A. 5e2x+x5e^{2x}+x
    • B. 10e2x+1x10e^{2x}+\frac1x
    • C. 10e2x+ln⁡x10e^{2x}+\ln x
    • D. 5e2x+1x5e^{2x}+\frac1x

  2. 2. Differentiate y=3xy=3^{x}.

    • A. x3x−1x3^{x-1}
    • B. 3x3^{x}
    • C. 3xln⁡33^{x}\ln3
    • D. 3xln⁡3\frac{3^{x}}{\ln3}

  3. 3. Find the gradient of y=cos⁡3xy=\cos3x at x=π6x=\frac{\pi}{6}.

    • A. 33
    • B. −3-3
    • C. 00
    • D. −32-\frac{3}{2}

  4. 4. Differentiate y=sin⁡4x−tan⁡xy=\sin4x-\tan x.

    • A. 4cos⁡4x−sec⁡2x4\cos4x-\sec^2x
    • B. cos⁡4x−sec⁡2x\cos4x-\sec^2x
    • C. 4cos⁡4x+sec⁡2x4\cos4x+\sec^2x
    • D. −4cos⁡4x−sec⁡2x-4\cos4x-\sec^2x

  5. 5. Which limit is used to prove ddx(sin⁡x)=cos⁡x\frac{d}{dx}(\sin x)=\cos x from first principles?

    • A. cos⁡h−1h→1\frac{\cos h-1}{h}\to1
    • B. sin⁡hh→0\frac{\sin h}{h}\to0
    • C. sin⁡h→1\sin h\to1
    • D. sin⁡hh→1\frac{\sin h}{h}\to1

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