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Differentiation

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Question 121

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]

Differentiation Questions

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

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) 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