What is Implicit Differentiation?
Example
Related Rates
- In related rates problems we investigate the effect that a change in a particular rate has on a different rate.
- There are many examples of this in real life, such as:
- The rate at which air is pumped into a balloon affects the rate at which the balloon's surface area changes.
- The rate at which water is released from a reservoir affects the rate at which the water level in a reservoir changes.
- The speed of a car affects the rate at which the car consumes fuel.
Solving Related Rates
- There aren't any specific rules to solving questions about related rates, yet there are a few tricks that can come in handy.
- These are:
- Drawing a diagram of the problem, including geometric shapes.
- Labeling the diagram with variables and fixed quantities.
- Identifying an equation that relates the variables.
- If you have more than two variables, identify another equation that allows you to express one of the variables in terms of the other by substituting it into the main equation.
- Differentiate your equation implicitly if needed.
- Find the unknown quantity.