The voltage V in volts, the current I in amperes, and the resistance R in ohms of an electric circuit like the one shown here are related by the equation V equal IR. Suppose that V is increasing at the rate of three volts per second. The fact that it's increasing tells us it's a derivative. It's changing. So DVDT is going to be 3 volts per second while I is decreasing DIDT. If it's decreasing, we're going to have a negative rate. It's going down of -1 third amps per second. Let T denote time in seconds. Answer the following questions. So DVDT is 3 volts per second. DIDT is -1 third amps per second. Now we want to do a relationship where we have Dr. over DT equaling things in terms of V's and i's. So DRDT, we're going to take the derivative of V equal IR and we get DDT of V equaling DTT of IR, remembering that we have to do the product role when we have the I * r So we have the derivative in terms of time of the I times the R Plus the derivative in terms of R of the I. So DVDT equal DID t * r + d RDT times I. The directions say we want to solve for DRDT, so we're going to subtract our DID t * r to the other side. We're going to divide by the I and that gets our DRDT by itself. But we wanted to relate it in terms of DVDT&DIDT. So we don't want R in the right hand or in the left hand side of this equation. We don't want R in the other side of whatever we're solving DRDT for. So when we go back to this original equation, if V equals IR, then v / I has to equal R. So we're going to take out the R down here and we're going to put in what R equals. So we're going to put in V / I. So the last part says when the Volt is 36 and the four is the amps, is the R increasing or decreasing and at what rate? So we're going to put in one over the current or 1 / 4 times the DVDT which the was the three volts per second minus -1 third the amps per second times the 36 volts over the four amps and that all equals our DRDT. If we do our computations, we get 1/4 times the quantity 3 + 3 DRDT. 3 + 3 is six, 6 / 4 is 3 halves, so 3 halves. DRDT is how it's changing, and because it's positive we know it's increasing. If it had been negative, it would have been decreasing.