a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4), has a value of 1. %3D Please input your answer as a column vector.

Q: Find the directional derivative of f(x,y, z) = xy + yz + zx at the point P(1, 1, 1) in the direction…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where а 3 (—3, —4, — 2), b — (—2, —5,…

A: Topic:- vector and it's derivatives

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = 1/θ and dθ/dt = t2

A: Given Data The position vector is r=1/θ. The change in angle vector is dθ/dt=t2=2t.   Integrate the…

Q: What is the gradient of a function f(x, y) and why might we want to calculate it? How does it relate…

A: Properties of gradient of function

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: (a) (10 pts.) Consider the function h(x, y) = r³ – x sin(2y – 2) + y? Calculate the derivative of…

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

A: Answer is mentioned below

Q: Which of the following is the directional derivative of f(r, y) = r'y at the point (-1,-1) in the…

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Q: Find the directional derivative of the function f (x, Y, z) = 6x² –- 2xy + yz in the direction of…

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Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

Q: In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer…

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Q: Calculate the directional derivative of f(x, y) = y – 2xy? at the point (0, 1) in the direction v =…

A: Solution

Q: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: Let f(x, y, z) = xy² 23 Find the directional derivative of the function at the point (1,-2,1) in the…

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Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

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

A: Givenf(x,y)=xx2+y2 , (2,1) , v=<3,5>

Q: Find the equation of the tangent plane to z=e^x+y+y^2+ 9 at the point (0,4,30)

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Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: Ex.: Find the directional derivative of the function f(x, y) x'y + x'y at the point (1,1) in the…

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Q: Find the directions in which the directional derivative of f(x, y) = ye at the poist (0, 2) has the…

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Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

Q: Let f (x, y) = x² + 4xy². Say the directional derivative Du(1,1) with u is the unit vector that…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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

A: Consider the following function: fx,y=eysinx Gradient of the function:…

Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: Let f(x, y, z) = xy + z*, P = (3, 9, 1). Calculate the directional derivative in the direction…

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

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Q: Find a unit vector in the direction in which f(x, y) = 6 cos(x – 5y) decreases most rapidly at P and…

A: Given, fx,y=6cosx-5y Find the unit vector and rate of change of f at P.

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

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Q: a) What is the rate of change of f(x, y) = 3xy + y^2  at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

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

A: Given that, gu,v=u2e-v,8,0 and v=3i+4j. Find the value of ∂g∂u and ∂g∂v at the point (8,0).…

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

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

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Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

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Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: 12. What is the directional derivative of f(r, y, z) = ba?y2² +x² + y? +22 in the direction of (8,…

A: Given that fx,y,z=bx2y2z2+x2+y2+z2 in the direction (8,9,12) find out the directional derivative

Q: Which of the following is the directional derivative of f(r, y) = z'y at the point (-1,-1) in the…

A: The directional derivative formula is given by Duf(x,y)=∇f(x,y)⋅u, where u is the unit vector and…

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

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Q: Which of the following is the directional derivative of f(r, y) at the point (0,0) in the direction…

A: Formula to find the directional derivatives helps to find the required directional derivative in the…

Q: If asked to find the directional derivative of f(r, y) in the direction of a NON unit vector (a…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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

A: Finding the directional derivative of the given function

Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

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

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Q: Calculate the directional derivatives of functions f(x, y)= x? – y? .2 in the direction of the…

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, 3, 2), b = (1,2,…

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

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

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Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,