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Differentiation

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Question 199

Given that x x\,x is measured in radians,

Prove, from first principles, that the derivative of sin(x)sin (x)sin(x) is cos(x)cos (x)cos(x), using the formula for sin(A±B)sin (A \pm B)sin(A±B) and the facts that as h→0h \rightarrow 0h→0 sin⁡hh→1\displaystyle \frac{\sin h}{h} \rightarrow 1hsinh​→1 and cos⁡h−1h→0\displaystyle \frac{\cos h - 1}{h} \rightarrow 0hcosh−1​→0.

[5]
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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