Question

Find the directional derivative of f(x,y)=√xy​ at P(9,1) in the direction from P to Q(12,−3).

Answer 1

To find the directional derivative of f(x,y)=√xy at P(9,1) in the direction from P to Q(12,−3), we can use the formula Dvf = ∇f · u.

Step-by-step explanation:

To find the directional derivative of the function f(x,y) = √xy at point P(9,1) in the direction from P to Q(12,-3), we can use the formula: Dvf = ∇f · u, where Dvf is the directional derivative, ∇f is the gradient of f, and u is the unit vector in the direction from P to Q.

Step 1: Calculate the gradient of f(x,y) = √xy.

Step 2: Calculate the unit vector u from P to Q.

Step 3: Compute the dot product ∇f · u.

Step 4: The result is the directional derivative of f(x,y) = √xy at point P(9,1) in the direction from P to Q(12,-3).