c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x, y, z) at the point Q(1, 2, ³) i in the direction of a = 2 i-2j+ k. Hence, obtain the direction and the value of maximum change of p(x, y, z) at the point Q.

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the…

A:

Q: Find the direction for which directional derivative of f (x,y) = 3x² – 4xy + 2y² +29 at (-2,3) is…

A: Formula: The maximum directional derivative of f(x, y) at (a, b) is given by ∇f(a, b) and direction…

Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.