Given differential of the function f at the point (3,2) 2. df = 3dr + ddy Find the directional derivative f, at the point (3,2) in the direction of the vector T = -27 +37.

Q: 3. Let f(x, y) = x² – y². Find a unit vector i for which D7f(3, 4) Dif (3,4) is the directional…

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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 velocity and acceleration vectors of the particle whose position at time t seconds is given…

A: We have a given position vector of any particle. And we have to find velocity and acceleration…

Q: 1. Given f(xiy)=J 2+x²+2y², the point p(2,1), and vector i = < a) Find the directional derivative at…

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Q: The directional derivative of x,y) - 16/x - 13y at the point (11,8) in the direction of the given…

A: The direction derivative  of f(x,y) in the direction of unit vector, is defined as follows.

Q: Find the directional derivative at (1,0) if Vƒ(1,0) = in the direction of the unit vector u = i?…

A: Given : ∇f(1,0)=&lt;-4,3&gt;   To Find: directional derivative at (1,0) in the direction of the unit…

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

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Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

Q: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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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: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=&lt; tan(2t) ,sec(5t) , 1/t^3&gt;…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

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 directional derivative of the function h at the point (1,1,1) in the direction of vector…

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

A: Please refer the attached image for complete solution.

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

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Find the second derivative of the vector-valued function #(t) = (6t + 4 sin(t))i + (5t + 7 cos(t))3…

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

A: In this first we calculate derivative of g function then get a unit vector in the direction of v. So…

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

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Q: Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the…

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

A: The objective is to find the directional derivative of the given function h(r,s,t) along the point…

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If R(0) = (-1,4,-5),…

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Q: Find the Directional Derivatives of f (x, y) = ey at (2, 3) in the direction v = 3i – 4j

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Q: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x -…

A: Given function is w=x2-3xy-y2+2xz2+6yz

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-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.…

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: Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w =…

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Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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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: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t-…

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Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =…

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function.…

Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

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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: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x3 –…

A: Directional derivative are given by gradient of function

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

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Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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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 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: p1. Find the directional derivative of o = x²z+ 2xy² + yz? at (1, 2,-1) in the direction of vector…

A: on using gradient we get

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: Given the temperature function z= T(x,y) implicitly defined by the equation r--z+yz'se sen(xy-2)-0…

A: Given the equation ex-1y2-z+yz2senxy-2=0