Thread: How to apply differentiation here?

Under ideal conditions, a perfect gas satisfies the equation PV=K ( where P is pressure, V is

volume and K is a constant ). If K=60 and pressure is found by measurement to be 1.5 units

with an error of 5% per unit,find approximately the error in calculating V.

Originally Posted by Vinod

Under ideal conditions, a perfect gas satisfies the equation PV=K ( where P is pressure, V is

volume and K is a constant ). If K=60 and pressure is found by measurement to be 1.5 units

with an error of 5% per unit,find approximately the error in calculating V.

The error is given by the exact change in volume divided by the volume.



This, in general, is hard to calculate so we approximate it with



Now if we take the derivative using the product rule we get

plugging this into the above gives



Since the 5% can be positive or negative we get that the approximate error is