2. Find the directional derivative of f(x,y, z) = x²y + yz² at P(1,–1,3) in the direction of vector (1,5, 2). -2 a) V30 3 b) V30 V30 7 d) 30 e) None of the above

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

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: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

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

A:

Q: of f(x, y, tion of ve

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

A:

Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

A:

Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

A:

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

A:

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

A:

Q: f f(x, y, z) = xy: on of vectorî - %3D

A:

Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

A:

Q: Suppose z is implicitly given by the equation x³y-yz²+ -5 x In a neighborhood of the point P(1, 1),…

A:

Q: Find the directional derivative at (1, 1) if Vƒ(1, 1) = (3,−1) in the direction of the unit vector u…

A: Use the formula of directional derivative.

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

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: rative of the f he unit vecto p, then Ja + B|

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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 f(x,v) at point p in the direction of vector a. 1)…

A: