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>0Determine an expression for dPdT\frac{dP}{dT}dTdP in terms of TTT and PPP.
Find the exact value of the rate of change of pressure with respect to temperature when T=0T = 0T=0.
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.
