Implicit Differentiation

**calculus shmalculus** · October 24th 2008, 11:29 AM

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4=C where C is a constant. Suppose that at a certain instant the volume is 510 cubic centimeters and the pressure is 81kPa and is decreasing at a rate of 7 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

how do approach this problem?

**galactus** · October 24th 2008, 12:20 PM

Differentiate your equation wrt time.

$P\cdot V^{1.4}=C$

$P\cdot 1.4V^{0.4}\cdot \frac{dV}{dt}+V^{1.4}\cdot \frac{dP}{dt}=0$

Enter in all your knowns and solve for dV/dt

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