Calculus Involving Inverse Trig (Edexcel A-Level Further Mathematics): Quizzes

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Calculus Involving Inverse Trig
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What is ddx(arcsin⁡x)\frac{d}{dx}(\arcsin x)?

11−x2\frac{1}{\sqrt{1-x^2}}

What is ddx(arccos⁡x)\frac{d}{dx}(\arccos x)?

−11−x2-\frac{1}{\sqrt{1-x^2}}

What is ddx(arctan⁡x)\frac{d}{dx}(\arctan x)?

11+x2\frac{1}{1+x^2}

What is ddx(arccotx)\frac{d}{dx}(\text{arccot} x)?

−11+x2-\frac{1}{1+x^2}

What is the domain restriction for arcsin⁡x\arcsin x and arccos⁡x\arccos x?

∣x∣≤1|x| \leq 1

Which of these derivatives is positive?

ddx(arcsin⁡x)\frac{d}{dx}(\arcsin x)

What is ddx(12arctan⁡(x2))\frac{d}{dx}\left(\frac{1}{2}\arctan(x^2)\right)?

x1+x4\frac{x}{1+x^4}

What is ddx(xarccos⁡x)\frac{d}{dx}(x\arccos x)?

arccos⁡x−x1−x2\arccos x - \frac{x}{\sqrt{1-x^2}}

What is ddx(arcsin⁡x+x1−x2)\frac{d}{dx}(\arcsin x + x\sqrt{1-x^2})?

11−x2+1−x2\frac{1}{\sqrt{1-x^2}} + \sqrt{1-x^2}

What is the domain restriction for arcsecx\text{arcsec} x?

∣x∣>1|x| > 1

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