Differentiation
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For a real variable ttt, use the quotient rule and the known derivatives of sin⁡t \sin t\,sint and cos⁡t \cos t\,cost to demonstrate that:

a.
ddt(tan⁡t)=sec⁡2t \frac{d}{dt}(\tan t) = \sec^2 t dtd​(tant)=sec2t
[3]
b.
ddt(sec⁡t)=sec⁡ttan⁡t \frac{d}{dt}(\sec t) = \sec t \tan t dtd​(sect)=secttant
[3]
c.
ddt(cot⁡t)=−csc⁡2t \frac{d}{dt}(\cot t) = -\csc^2 t dtd​(cott)=−csc2t
[3]
d.
ddt(csc⁡t)=−csc⁡tcot⁡t \frac{d}{dt}(\csc t) = -\csc t \cot t dtd​(csct)=−csctcott
[3]

Differentiation Questions

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 100 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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Differentiation Questions

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