1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction of a unit vector whose angle with the semi-axis x is 1, u = cos i + sen j b. f(x,y) = x²-xy + 3y² at the point (-1,-2) in the direction of a unit vector whose angle with the semi-axis x is u = cos 0 i+sen j c. f(x,y) = x²sin y at the point (1.1) in the direction of a vector v = 3i-4j

Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction…

A: Here we have to find the directional derivative for given f(x, y, z).

Q: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

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

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Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

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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.

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Consider the function f(x,y) = 3- a. Fill in the table with the values of the directional derivative…

A: Here to find the directional derivative at (a, b) of fin(x, y) the direction of unit vector u, v and…

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…