f(x, y) = -0.02a²y³ a) Compute V f. Vf = ( b) Find the derivative of f at the point P( – 3, – 2) in the direction of ü = ( – 1, – 1) fu( – 3, – 2) - c) In which direction is the largest directional derivative? Please give a unit vector in this direction %3D max

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: 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: 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: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

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 of the function at the given point in the direction of the vector v.…

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

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Q: Find the directions in which f increases and decreases most rapidly at P.. Also, find the derivative…

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

A: The given function is fx,y=7exsiny.    point: 0,π3   and   direction vector: v=-10, 24. Obtain the…

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

A: Solution is given below

Q: 5. For a given function f(x, y) = Vx² +y² , what is the directional derivative of f at any point…

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Q: at the point (0,0) 1+y Which of the following is the directional derivative of f(2, y) in the…

A: The gradient is the partial derivative of a multivariable function. The gradient of a function tells…

Q: Q1. Calculate the directional derivative of f (x, y, z) of vector v =i+2j+3k. = xyz at point P =…

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

Q: consider the function f(x, y) esin(@) y Find the directional derivative of f at the point (, 1) in…

A: Please refer the attached image for complete solution.

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: Calculate the directional derivatives of the function x²y x²+ y? for (x, y) +0 f(x,y) = for (x, y)…

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Q: Again just working on examples for exam, would like to see how you solve this to see if it is 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 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: Consider the function 422 + Vy+3z . f(x, y, z) = 3x – 7 Find the directional derivative of f at the…

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

A: Applications of derivatives

Q: Find the directional derivative D, f(2, –3, -3) for the function f(x, y, z) = ry + yz + zx in the…

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Q: Find the directional derivative of the function f(x, Y, z) = x + ln(y² + z²) at the point A(2,1, 1)…

A: To find the directional derivative of the function f(x,y,z)=x+ln(y2+z2) at point A(2,1,1)  in the…

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

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

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 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: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: h (r, s, t) = ln (3r + 6s + 9t), (1, 1, 1), v = 4i+ 12j + 6k

A: We have hr,s,t=ln3r+6s+9t at 1,1,1 in the direction of v=4i+12j+6k

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

A: This is a problem of Vector Calculus.

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: 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: Compute the directional derivative of f at the given point in the direction of the indicated vector.…

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Q: 7. Let f(x,y)=9-x² – y² a. Find the maximum value of the directional derivative at the point (1,2)…

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

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Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

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

A: Solution-

Q: 2. Find the directional derivative of f(x,y, z) = x²y + yz² at P(1,–1,3) in the direction of vector…

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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…

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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: The temperature T, at a point (x, y) in the xy-plane is given by T(x, y) = 4x^2y^3 degrees Celsius.…

A: We have to find a unit vector in the direction in which the temperaturedecreases most rapidly at (2,…

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

A: To find the directional derivative of the function at a point in the direction of the given vector,…

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.

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 the function at the given point in the direction of the vector v.…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.