Differentiating inverse trigonometric and hyperbolic functions

Differentiating inverse trigonometric and hyperbolic functions Quiz

Spec 3.2 · Edexcel International A Level Further Maths: Quiz

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  1. 1. Find ddxarcsin⁡3x\frac{d}{dx}\arcsin3x.

    • A. 11−9x2\frac{1}{\sqrt{1-9x^2}}
    • B. 31−9x2\frac{3}{\sqrt{1-9x^2}}
    • C. 31−3x2\frac{3}{\sqrt{1-3x^2}}
    • D. 39x2−1\frac{3}{\sqrt{9x^2-1}}

  2. 2. Find ddxarctan⁡(x2)\frac{d}{dx}\arctan\left(x^2\right).

    • A. 11+x4\frac{1}{1+x^4}
    • B. 2x1+x2\frac{2x}{1+x^2}
    • C. x1+x4\frac{x}{1+x^4}
    • D. 2x1+x4\frac{2x}{1+x^4}

  3. 3. Find ddxarcosh⁡(2x)\frac{d}{dx}\operatorname{arcosh}(2x) for x>12x>\frac12.

    • A. 24x2−1\frac{2}{\sqrt{4x^2-1}}
    • B. 14x2−1\frac{1}{\sqrt{4x^2-1}}
    • C. 21−4x2\frac{2}{\sqrt{1-4x^2}}
    • D. 24x2+1\frac{2}{\sqrt{4x^2+1}}

  4. 4. Find ddx(12artanh⁡x2)\frac{d}{dx}\left(\frac12\operatorname{artanh}x^2\right).

    • A. x1+x4\frac{x}{1+x^4}
    • B. 11−x4\frac{1}{1-x^4}
    • C. x1−x4\frac{x}{1-x^4}
    • D. 2x1−x4\frac{2x}{1-x^4}

  5. 5. Find ddx(xarsinh⁡x)\frac{d}{dx}\left(x\operatorname{arsinh}x\right).

    • A. x1+x2\frac{x}{\sqrt{1+x^2}}
    • B. arsinh⁡x+x1+x2\operatorname{arsinh}x+\frac{x}{\sqrt{1+x^2}}
    • C. arsinh⁡x+11+x2\operatorname{arsinh}x+\frac{1}{\sqrt{1+x^2}}
    • D. arsinh⁡x−x1+x2\operatorname{arsinh}x-\frac{x}{\sqrt{1+x^2}}

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