Plugging a specific value for the time variable into the function for power would then yield the power consumption of our home during a specified hour. If we were to take the derivative of this function, we would get a function of power with respect to time. If we were to record the average energy usage of our home (in kWh) for each hour of a day, we would likely get a composite function characterizing energy consumption with respect to time. Let's say that we are interested in installing auxiliary power sources for our home such as a solar panel array or a generator.

Now that we have a better understanding of energy and power, let's go back to our example. If we consumed 1000 Joules of energy per second, we would have 1,000 W (1 kW) of power consumption. Power is the amount of energy consumed per unit time. So, if we were to run a single 1000 W microwave oven for 1 hour, we would consume 1 kWh of energy (1,000 W = 1 kW). A watt, commonly notated with a 'W', is a unit of measurement for power. A kWh is a unit of energy (energy is the ability to do work). When reading the electrical meter for a home, we see that we are given the unit of kWh, or kilowatt-hour.

Solar Panel Arrayįirst, a little background information on energy and power. Having the ability to take the derivative of a function composed of other functions is valuable, especially when it saves us from having to expand functions like ( x 2-3 x+10) 9 before taking the derivative.īut how can the Chain Rule help us when we are not in the classroom? To answer this question, let's consider power consumption in our home at specific times, and in turn, using this information to evaluate the infrastructure requirements for a solar panel array or a generator. When we are in our calculus classes, the Chain Rule is extremely helpful when working with composite functions.

Chain rule calculus with steps