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)=limh0f(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

limh0sin(h)h\lim_{h \to 0} \frac{\sin(h)}{h}

11

limh0cos(h)1h\lim_{h \to 0} \frac{\cos(h) - 1}{h}

00

ddx(sinx)\frac{d}{dx}(\sin x)

cosx\cos x

ddx(cosx)\frac{d}{dx}(\cos x)

sinx-\sin x

ddx(tanx)\frac{d}{dx}(\tan x)

sec2x\sec^2 x

ddx(secx)\frac{d}{dx}(\sec x)

secxtanx\sec x \tan x

ddx(cotx)\frac{d}{dx}(\cot x)

csc2x-\csc^2 x

ddx(cscx)\frac{d}{dx}(\csc x)

cscxcotx-\csc x \cot x

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