Final answer:
The directional derivative of the function g(s, t) = st at the point (2, 4) in the direction of the vector v = 3i - j is 2.
Step-by-step explanation:
To find the directional derivative of the function g(s, t) = st at the point (2, 4) in the direction of the vector v = 3i - j, we can use the formula:
Directional derivative = ∇g · v
where ∇g is the gradient vector of g and · represents the dot product. In this case, the gradient of g is ∇g = (t, s) and the vector v = (3, -1).
Substituting the values, we get:
Directional derivative = (2, 4) · (3, -1) = 2(3) + 4(-1) = 6 - 4 = 2.