Further Differentiation (Edexcel A-Level Mathematics): Quizzes

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Differentiating Reciprocal and Inverse Trig Functions
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What is ddxcsc(x)\frac{d}{dx} \csc(x)?

csc(x)cot(x)-\csc(x) \cot(x)

What is ddxsec(x)\frac{d}{dx} \sec(x)?

sec(x)tan(x)\sec(x) \tan(x)

What is ddxcot(x)\frac{d}{dx} \cot(x)?

csc2(x)-\csc^2(x)

What is ddxarcsin(x)\frac{d}{dx} \arcsin(x)?

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

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

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

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

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

Which rule is used to derive reciprocal trig function derivatives?

Quotient rule

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

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

What is ddxarcsec(x)\frac{d}{dx} \text{arcsec}(x)?

1xx21\frac{1}{|x| \sqrt{x^2 - 1}}

What is ddxarccsc(x)\frac{d}{dx} \text{arccsc}(x)?

1xx21-\frac{1}{|x| \sqrt{x^2 - 1}}

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