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)=limh0f(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)=sinxcosh+cosxsinh\sin(x+h)=\sin x\cos h+\cos x\sin h

What is limh0sin(h)h\lim_{h \to 0} \frac{\sin(h)}{h} equal to?

11

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

00

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

cosx\cos x

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

sinx-\sin x

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

sec2x\sec^2 x

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

secxtanx\sec x \tan x

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

csc2x-\csc^2 x

What is ddx(cos2x)\frac{d}{dx}(\cos^2 x)?

2sinxcosx-2\sin x \cos x

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