Chapter 4: Partial Differentiation
Section 4.4: Directional Derivative
Example 4.4.8
At point P, the directional derivative of in the direction is 8, but in the direction , it's . Find the directional derivative of in the direction .
Solution
Mathematical Solution
The unknowns in this example are , , and . The gradient of at P can be found from the known values of the directional derivatives in the directions u and v. From this, the value of the directional derivative in the direction w can be computed.
From the first two equations, , from which it follows that
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Context Panel: Assign Name
Obtain and solve the equations , and
Common Symbols palette: Dot product operator
Context Panel: Solve≻Solve
Context Panel: Select Element≻3
Context Panel: Combine≻radical
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Define the vectors , u, v, and w.
Form the three equations
Apply the DotProduct and Normalize commands.
Solve for , and
Apply the solve command, then the combine command to simplify the resulting radicals
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