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Related rates problems are an application of derivatives and implicit differentiation that allow us to figure out how fast one thing is changing in relation to how fast something else is changing. For example, we might be interested in how fast the top of a ladder is sliding down a wall compared to how fast the bottom of the ladder is sliding away from the wall.
Related rates problems allow us to do that by using implicit differentiation. We’ll usually take the derivative of the equation, taking the derivative of every variable with respect to time t. Then we’ll plug in for what we know and solve for the value we’re interested in.
The key to related rates problems is getting the right equation set up. You need to figure out what equation you can write that will include the value you need to solve for. In addition to that, you may have to come up with a second equation that will give you the value for a missing variable that you need to plug into your first equation.