Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at point (1, -1, 2) in the direction given byy = -i+ 2j +k. Show the graph after it.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given function is, f(x,y)=sin(2x+y) and u=cos(-5π6)i+sin(-5π6)j⇒u=cos(5π6)i-sin(5π6)j=-32i-12j Now,…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find the directional derivative of the function at a given point in a unit direction.

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 at (1,0) if Vƒ(1,0) = in the direction of the unit vector u = i?…

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

Q: Find the directional derivative off at the given point in the direction indicated by the angle 0.…

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Q: Find the directional derivative of the function f (x, y) = 7x² – 2.xy at the point P,(-3,5) in the…

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

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

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

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Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P…

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Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

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Q: Find a unit vector in the direction in which f (x, y) = 8 cos(5x – 3y) decreases most rapidly at P…

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

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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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: 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)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction…

A: Firstly, we calculate unit vector in direction of vector u.

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

A: The function is given as f(x,y)=5xy . The point is x=2 and y=8 inclined at angle θ=π3. The…

Q: 4 3 Compute the directional derivative of the function g(x.y)= sin (T(X – 6y)) at the point P(2,3)…

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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: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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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 +…

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

A: Answer

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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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: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: For f(z, y) is: = 5a sin(xy) at the point (2, 4), the direction in which the maximum rate of change…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Answer is given below

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: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find out the directional derivative.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: This question can be solved using the concept of the stated theorem 13.9

Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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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: (#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: 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 for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

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Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

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: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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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 f(r, y) = 1+5x/j at the point (5, 1) in the…

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Q: Find the directional derivative of the function f(x, y) = x²y° in the direction of the vector at…

A: Concept:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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

A: First we find partial derivative with respect to x and y.