Chapter 4.5, Problem 256E

The total resistance in a circuit that has three individual resistances represented by x. y. and z is given

by the formula $R\left(x,y,z\right)=\frac{xyz}{yz+xz+xy}$ . Suppose at a

given time the x resistance is 100 $\Omega$ . the y resistance is 200 $\Omega$ . and the z resistance is 300 $\Omega$ . Also, suppose the v resistance is changing at a rate of 2 $\Omega$ /min. the y resistance is changing at the rate of 1 $\Omega$ /min. and the z resistance has no change. Find the rate of change of the total resistance in this circuit at this time.