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Differentiation

Differentiation

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Question 4

Use the derivatives of sin⁡(x)\sin(x)sin(x) and cos⁡(x)\cos(x)cos(x) to show that:

a.

Write tan⁡x \tan x\,tanx in terms of sin⁡x \sin x\,sinx and cos⁡x\cos xcosx.

[1]
b.
ddx(tan⁡x)=sec⁡2x \frac{d}{dx}(\tan x) = \sec^2 x dxd​(tanx)=sec2x
[3]
c.
ddx(sec⁡x)=sec⁡xtan⁡x \frac{d}{dx}(\sec x) = \sec x \tan x dxd​(secx)=secxtanx
[3]
d.
ddx(cot⁡x)=−csc⁡2x \frac{d}{dx}(\cot x) = -\csc^2 x dxd​(cotx)=−csc2x
[3]
e.
ddx(csc⁡x)=−csc⁡xcot⁡x \frac{d}{dx}(\csc x) = -\csc x \cot x dxd​(cscx)=−cscxcotx
[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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