1.9.16 Implicit differentiation (A-level only)

The relationship between the temperature $T$ and the pressure $P$ of a contained gas is modeled by the equation

2P^2 + TP^2 = 5(4^T) + 13, \quad P > 0

a.

Determine an expression for $dPdT\frac{dP}{dT}$ in terms of $T$ and $P$ .

[4]

b.

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

[4]

The relationship between the temperature $T$ and the pressure $P$ of a contained gas is modeled by the equation

2P^2 + TP^2 = 5(4^T) + 13, \quad P > 0

a.

Determine an expression for $dPdT\frac{dP}{dT}$ in terms of $T$ and $P$ .

[4]

b.

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

[4]

1.9.16 Implicit differentiation (A-level only) Questions