Use the Related Rate Calculator to find a rate of change such as dy/dx (rate of y with respect to x) or dy/dt (rate of y with respect to time t) using the chain rule. Enter any two values in a tab to calculate the missing one.
Related Rate Formula
The following two example problems outline the steps and information needed to calculate a rate of change such as dy/dx.
\frac{dy}{dx}=\frac{\Delta y}{\Delta x} \qquad \frac{dy}{dt}=\frac{dy}{dx}\cdot\frac{dx}{dt}- Where Δx is the change in x and Δy is the change in y.
- dy/dx is the rate of change of y with respect to x (slope).
- If x and y both depend on time t, then dy/dt can be found using the chain rule dy/dt = (dy/dx)(dx/dt).
To estimate dy/dx from finite changes, divide Δy by Δx. For classic calculus “related rates” problems (ladder, circle, sphere, etc.), you typically differentiate a relationship with respect to time to connect dy/dt and dx/dt.
How to Calculate Related Rate?
The following example problems outline how to calculate a related rate.
Example Problem #1:
- First, determine the change in y (Δy).
- The change in y is given as: 40.
- Next, determine the change in x (Δx).
- The change in x is provided as: 80.
- Finally, calculate the rate dy/dx using the equation above.
dy/dx = Δy / Δx
The values provided above are inserted into the equation below and computed.
dy/dx = 40 / 80 = 0.50
Example Problem #2:
For this problem, the variables required are provided below:
change in y (Δy) = 60
change in x (Δx) = 80
Test your knowledge using the equation and check your answer with the calculator.
dy/dx = Δy / Δx = ?
