Question

If f(x, y, z) = x sin(yz), find the directional derivative at the point (a, b, c) in the direction of vector (u, v, w).

A. u cos(bc) + vab cos(bc) + wab sin(bc)
B. u sin(bc) + vab sin(bc) + wab cos(bc)
C. u cos(bc) - vab sin(bc) + wab cos(bc)
D. u sin(bc) - vab cos(bc) + wab sin(bc)

Answer 1

The directional derivative of a function f(x, y, z) = x sin(yz) at the point (a, b, c) in the direction of vector (u, v, w) is (u * cos(bc)) + (vab * cos(bc)) + (wab * sin(bc)).

Step-by-step explanation:

The directional derivative of a function f(x, y, z) = x sin(yz) at the point (a, b, c) in the direction of vector (u, v, w) can be found using the formula:

Directional derivative = (u * cos(bc)) + (vab * cos(bc)) + (wab * sin(bc))

Therefore, the correct answer is A. u cos(bc) + vab cos(bc) + wab sin(bc).