First Principles Differentiation - Trigonometry (AQA A-Level Mathematics): Quizzes

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First Principles Differentiation - Trigonometry
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What does the limit definition f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} represent?

Slope of tangent line

What is the sine addition formula?

sin⁡(x+h)=sin⁡xcos⁡h+cos⁡xsin⁡h\sin(x+h)=\sin x\cos h+\cos x\sin h

What is lim⁡h→0sin⁡(h)h\lim_{h \to 0} \frac{\sin(h)}{h} equal to?

11

What is lim⁡h→0cos⁡(h)−1h\lim_{h \to 0} \frac{\cos(h) - 1}{h}?

00

What is ddx(sin⁡x)\frac{d}{dx}(\sin x) from first principles?

cos⁡x\cos x

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

−sin⁡x-\sin x

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

sec⁡2x\sec^2 x

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

sec⁡xtan⁡x\sec x \tan x

What is ddx(cot⁡x)\frac{d}{dx}(\cot x) from the formula sheet?

−csc⁡2x-\csc^2 x

What is ddx(cos⁡2x)\frac{d}{dx}(\cos^2 x)?

−2sin⁡xcos⁡x-2\sin x \cos x

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