The electrical potential (voltage) in a certain region of space is given by the function V(x, y, z) = 5x² –- 3xy + xyz. a. Find the rate of change of the voltage at point (3,4,5) in the direction of the vector (1,1,–1). b. In which direction does the voltage change most rapidly at point (3,4,5)?

Q: The directional derivative of x,y) - 16/x - 13y at the point (11,8) in the direction of the given…

A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: x, y, z) are the coordinates of the points inside the box. (a) Find the rate of change at the point…

A: The detailed solution of the problem is given in the next steps.

Q: f(x, y, z)=1/√√√x² + y² + z² P(-1,2,2) = -3i+27-3k

A:

Q: Let f(x, y, z) = xy sin(xz). The rate of change of f at the point P(1, -2, π) in the direction of…

A:

Q: Calculate the directional derivative of g(x, y, z) = z² – xy + 4y in the direction v = (1, –3, 2) at…

A: To find the directional derivative of g(x,y,z) in the direction of vector v at point P, first we…