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Differentiation

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Question 202

A calculus student is verifying the derivative formulas for trigonometric functions of uuu. Using the derivatives ddu(sin⁡u)=cos⁡u\displaystyle \frac{d}{du}(\sin u) = \cos udud​(sinu)=cosu and ddu(cos⁡u)=−sin⁡u\displaystyle \frac{d}{du}(\cos u) = -\sin udud​(cosu)=−sinu, help them prove that:

a.
ddu(tan⁡u)=sec⁡2u \frac{d}{du}(\tan u) = \sec^2 u dud​(tanu)=sec2u
[3]
b.
ddu(sec⁡u)=sec⁡utan⁡u \frac{d}{du}(\sec u) = \sec u \tan u dud​(secu)=secutanu
[3]
c.
ddu(cot⁡u)=−csc⁡2u \frac{d}{du}(\cot u) = -\csc^2 u dud​(cotu)=−csc2u
[3]
d.
ddu(csc⁡u)=−csc⁡ucot⁡u \frac{d}{du}(\csc u) = -\csc u \cot u dud​(cscu)=−cscucotu
[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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