Find the directional derivative of f(x, y, z) = -4x? + ly? – 4z2 at the point (0, -4, 2) in the direction of the origin.

Q: find the gradient of the function and the maximum value of th directional derivative at the given…

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Q: (a) Find the directional derivative of f (x,y) = In(xy) at (-) in the direction of (1,1).

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

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Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: Find the directional derivative of f(x, y) = 3x² - 2y² at point ,0) to point 3 (-2-1,0) 0(0,1). in…

A: Let's find directional derivative.

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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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…

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Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then  dot product with divergent of f(x,y)…

Q: Find the directional derivative of f(x, y) = 3x2 − 2y2 at (−3/ 4, 0) in the direction from P(−3/4,…

A: The directional derivative is the scalar product of the derivative of the function to the vector…

Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

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Q: Find the directions in which the directional derivative of f(x,y) = x^2 + xy^3 at the point (2,1)…

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Q: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

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Q: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

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

A: Formula to find the directional derivative in the direction of the given vector helps to find the…

Q: Find the directional derivative of the function f(x,y) = y² Inx at the point (1,2) in the direction…

A: Given function, f(x,y)=y2 ln x Point 1,2 and vector u=3,4 The unit vector of u is…

Q: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

A: Solution a: Given function is f(x, y)=xy+y Now gradient of the function is ∆f(x, y)=∂f∂x, ∂f∂y⇒∆f(x,…

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: Compute the directional derivative of the function f(x,y, z) = 3ryz at the point P: (1, –3, –1) in…

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Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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Q: Find the directional derivative of f(x, y) = Vxy at P(9, 1) in the direction from P to Q(12, -3).…

A: Given that: f(x,y)=xy        at P(9,1) in the direction of Q(12,-3)

Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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Q: Find the directional derivative of f(x, y) = x 2 + 4y 2 at the point P = (3, 2) in the direction…

A: Given, f(x,y)=x2+4y2 at the point P=(3,2)

Q: Find the directional derivative of the function f(x, y) =1+5zj at the point (5, 1) in the direction…

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Q: Find the directional derivative of f(x, y) = 3x² - y² + 5xy at (2,-1) in the direction of -3i - 4j.

A: given function f(x,y)=3x2-y2+5xy given point (2, -1) given direction u→=-3i-4j We have to find the…

Q: Find the direction in which the directional derivative of f(x, y) = x? + sin(xy) at the point (1,0)…

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Q: Find the directional derivative of f(x, y, z) = xz + y°, at (3, 2, 1) in the direction of 3 = 1+3+…

A: We need to find gradient of f at point (3,2,1)

Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7).…

A: Given function: fx,y,z=xy2z3

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Let f(x, y) = sin(x – y). Calculate the directional derivative of f in the direction of v = (1, 1)…

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Q: Find the directional derivative of f(x,y) = sin(x+2y) at the point (1, -3) in the direction θ=3π/4

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

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Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

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Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

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Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(4, 1, 1) in the direction of Q(0, –7, 9).…

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Q: Find the directional derivative of the function f(x, y) = √√√x + 2y at the point (2, 1) in the…

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Q: Find the directional derivative of the function f(x, y) = In(x + y²) at the point (1, - 1) in the…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y*) at the point (2, 1) in the…

A: we will find the directional derivative

Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

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