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Differentiation

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Question 473

The relationship between the temperature TTT and the pressure PPP of a contained gas is modeled by the equation

7T+2P2+TP2=5(4T)+13,P>0 7T + 2P^2 + TP^2 = 5(4^T) + 13, \quad P > 0 7T+2P2+TP2=5(4T)+13,P>0
a.

Determine an expression for dPdT\frac{dP}{dT}dTdP​ in terms of TTT and PPP.

[4]
b.

Find the exact value of the rate of change of pressure with respect to temperature when T=0T = 0T=0.

[4]
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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