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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 46

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]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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