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

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First Principles Differentiation - Trigonometry
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First principles derivative formula

f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

Geometric meaning of derivative

Slope of the tangent line to the curve

lim⁡h→0sin⁡(h)h\lim_{h \to 0} \frac{\sin(h)}{h}

11

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

00

ddx(sin⁡x)\frac{d}{dx}(\sin x)

cos⁡x\cos x

ddx(cos⁡x)\frac{d}{dx}(\cos x)

−sin⁡x-\sin x

ddx(tan⁡x)\frac{d}{dx}(\tan x)

sec⁡2x\sec^2 x

ddx(sec⁡x)\frac{d}{dx}(\sec x)

sec⁡xtan⁡x\sec x \tan x

ddx(cot⁡x)\frac{d}{dx}(\cot x)

−csc⁡2x-\csc^2 x

ddx(csc⁡x)\frac{d}{dx}(\csc x)

−csc⁡xcot⁡x-\csc x \cot x

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