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

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Calculus Involving Inverse Trig
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Derivative of arcsin⁡x\arcsin x

11−x2\frac{1}{\sqrt{1-x^2}}

Derivative of arccos⁡x\arccos x

−11−x2-\frac{1}{\sqrt{1-x^2}}

Derivative of arctan⁡x\arctan x

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

Derivative of arccotx\text{arccot} x

−11+x2-\frac{1}{1+x^2}

Derivative of arcsecx\text{arcsec} x

1∣x∣x2−1\frac{1}{|x|\sqrt{x^2-1}}

Derivative of arccscx\text{arccsc} x

−1∣x∣x2−1-\frac{1}{|x|\sqrt{x^2-1}}

Domain restriction for arcsin⁡x\arcsin x and arccos⁡x\arccos x

∣x∣≤1|x| \leq 1

Sign of arcsin⁡x\arcsin x derivative vs arccos⁡x\arccos x

arcsin⁡x\arcsin x positive, arccos⁡x\arccos x negative

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

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

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

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

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