You are given the derivative of a vector function r in the component form is dr (e,3e",-2t). You are also given that r(0)= 2i-j+k . dt a) Determine the vector function r (t) in the form r(t)= (x(t), y (t), z(t) An efficient notation for the vector equation of a straight line in 3D(or 2D) is given by ((t) = a + bt where t is any real number, a is the position vector from the origin to a point on the line and b

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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

A: The objective of the question is evaluate the directional derivative at the given point and…

Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

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Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

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Q: : Find the directional derivative of the following function, f(x, y, 2) = xy cos(10yz) at the point…

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Q: 2. Suppose that f (1,2)= 3 and that the directional derivative of fat point (1,2) in the direction…

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

Q: Find the directional derivative of f(x, y, z) = z3 – x²y at the point (5, -2, -2) in the direction…

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Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Find the directional derivative of the function at the point in the direction of the unit vector. 3…

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Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: : Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² + 2y²…

A: To find the directional derivative of the given function.

Q: Consider the function f (x, y) = 3 + 5x2 + 2y2, which is differentiable in an environment D from…

A: Given f (x, y) = 3 + 5x2 + 2y2

Q: ind the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2, -3, 6) in the…

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

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: 7. Find the directional derivative of the function f(x, y, z)=(y+28) at (2, 1, 1) in the direction…

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Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

Q: Find the directional derivative of the function f(, y) = In(x +y°) at the point (- 1,3) in the…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

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Q: Find the directional derivative of function f(x y)=x°e' at the point (1,1) and direction of vector…

A: Given:       fx,y=x2ey    at the point 1,1 and direction of vector v=2i      fxx,y=∂∂xx2ey…

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: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

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: #1. Find the directional derivative of the function f(x,y,z) = x²y + 2y2z at the point (1,–2,0) in…

A: Given:

Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

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Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

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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 direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Find the directional derivative of f(x, y, z) = z - x²y at the point (-3, -2, 4) in the direction of…

A: According to the Bartleby guidelines only one question can be solved at one time, post the second…

Q: Find the directional derivative of the function f(x, y) = In(x² + y*) at the point (– 3, – 1) in the…

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Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution

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

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Q: 3. Find the directional derivative of the function f (x, y)= sin (xy) at a point -2i +j in the…

A: The given function: f(x, y)=sin2(xy)P=34, πu→=-2i^+j^5

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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