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

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.

Question bank

1.4 A: Proof
1.5 B: Algebra and functions
1.6 C: Coordinate geometry in the (x, y) plane
1.7 D: Sequences and series
1.8 E: Trigonometry
1.9 F: Exponentials and logarithms
1.10 G: Differentiation
1.11 H: Integration
1.12 I: Numerical methods (A-level only)
1.13 J: Vectors