The directional Derivative of the given function is; -4/√37
Formula for directional derivative is given by;
D_u g(a, b) = ∇g(a, b) * u
where u is a unit vector
We are given;
g(p, q) = p⁴ - p²q³
∇g(p, q) = (dg/dp, dg/dq) = ((4p³ - 2pq³), (p⁴ - 3p²q²))
∇g(1, 1) = ((4(1)³ - 2(1 * 1³), (1⁴ - 3(1² * 1²))
∇g(1, 1) = (2, -1)
We are given v = i + 6j
Thus, unit vector of v is;
u = (i + 6j)/√(1² + 6²)
u = (i + 6j)/√37 = [1/√37, 6/√37]
Applying the directional derivative formula we have;
D_u g(1, 1) = ∇g(1, 1) * u
⇒ (2, -1) * [1/√37, 6/√37]
⇒ (2/√37) - (6/√37)
⇒ -4/√37
Read more about Directional Derivative at; https://brainly.com/question/9064150
