Final answer:
The directional derivative can be calculated by dotting the gradient of the function with a unit vector in the desired direction. If the function represents velocity, the directional derivative gives the acceleration. Sometimes the direction of the resultant vector is also relevant, which can be determined using trigonometric relationships.
Step-by-step explanation:
To calculate the directional derivative, you typically need the gradient of the function at a given point and the vector in the direction in which you're taking the derivative. The gradient is a vector of partial derivatives, and in physical problems, it can represent the rate of change with respect to spatial variables.
After finding the gradient, dot it with a unit vector in the direction of interest to find the directional derivative. However, using a calculator to find the directional derivative requires inputting the appropriate functions and following the calculator's procedures for computing derivatives and dot products.
If the function represents velocity, and you are looking for the acceleration, you would take the time derivative of the velocity function. If you have a position function, its first derivative with respect to time is the velocity, and the second derivative is the acceleration. When computing the velocity of an object, such as a taxi, you might need to calculate the gradient of the taxi's position function over time.
In more complex scenarios, including vectors, you may use graphical techniques or mathematical manipulations involving trigonometric relationships to determine the direction of the resultant vector, while calculating the acceleration of a medium could involve taking the partial derivative of the velocity equation with respect to time.