Problem 1 Consider the function: S(z, v) = sin(2z + 3y). (a) Find the gradient of f. 2. (b) Evaluate Vs at the point P=(-6,4). (c) Find the directional derivative at P in direction =(V3i-j).

Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y y.

A: As per the rules we can answer only the first question and rest can be reposted.

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

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

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Q: Problem 1. Find the directional derivative of f(r, y) = sin(x + 2y) at the point (3, 1) in the…

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Q: 18. Find the directional derivative of * f(x, y) = -2e* cos y at (0, 7) in the direction of v = (-6,…

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Q: In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the %3D…

A: We have to find maximum directional derivative.

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

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Q: Find the directional derivative of f at the given point in the indicated direction and write a…

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Q: Find the gradient of /x, y. 2) eand the largest value of the directional derivative of fox. y. zi…

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Q: Find the directions in which the directional derivative of f(x,y) = x^2 + xy^3 at the point (2,1)…

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Q: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3.

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Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: Consider the following equation.(1/2)(sqt(3)i-j) f(x, y) = sin(2x + 3y),    P(−6, 4),    u =   (a)…

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Q: Consider the function [cos: cos 30 Sin 30 x² x₁x₂-1 f(x)=x₂+- Determine the directional derivatives…

A: As per the question we are given the bivariate function f(x) = x2 + x1²/(x1x2 - 1) Now we have to…

Q: Find the directional derivative of f(x,y,z)=4x^2y-7z^3x+y^2 at the point (2,1,-1) in the direction…

A: We have to find the directional derivative of f(x,y,z)=4x^2y-7z^3x+y^2 at the point (2,1,-1) in the…

Q: The directional derivative of f(1, y) at the point P = (0, 4) in the direction of the origin is -2.…

A: Given directional derivative of fx,y at point P =(0,4) in the direction of O(0,0) is -2. Here,…

Q: A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point of…

A: Gradient, or slope of a line characterizes the direction of the line and is found out by dividing…

Q: Find the gradient of the function at the given point. Function Point f(x, y) = x2 + 2xy (2, 4) Vf(2,…

A: Given function fx,y=x2+2xyand the given point is 2,4.We need to find the maximum value of the…

Q: g(x, y) = 6x² – 3y², (/8, /5) Gradient is f(r, y) = tan 6y (16, 2) Gradient is

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Q: Problem 9. Find the derivative of the function at the point Po in the directic of the vector u: a)…

A: According to company rule we can answer only first question and rest can be reposted.

Q: QUESTION 7 3 4 Find the directional derivative of f(x,y) = 4xy – 3x + 2y in the direction u = at the…

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Q: Q1: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction of 4i – 3j…

A: (a) Given S=ln(2x+3y) Differentiate S partially with respect to x and y Sx=22x+3y…

Q: In(x) sin(y) 1. Let f(x, y) (a) Find Vf(x, y). (b) Find Vf(1,"/2). (c) Find the directional…

A: Solution

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

A: Here we have to find the directional derivative.

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (1, -4) in the direction 0 =…

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Q: Question 3 Consider the function f (x, y, z) = x- + y – xyz Find the directional derivative of f at…

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Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3. 7. -17 b= 19

A: Please refer to the image below

Q: Question 3 Consider the function h(x,y, z) = e10-xy + sin(2nz). (а) (i) Calculate the gradient of h.…

A: As per bartleby guidelines we only give first question answers with subpart.

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 ; P(-8,8); а%3…

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Q: The parametric equations of a curve are given by x = In (Vi +1) and y = cosh (2t). dy Find the…

A: Use chain rule of differentiation to solve this problem.

Q: In problem2 , find a vector in whose direction f(x,y,z) has zero change (zero derivative) at point…

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Q: Problem 4. Consider the function f : R² →R given by f(r, y) = y² – 2r². Find the directional…

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Q: Question 8 Let f (x, y, z) : = xz cos(y). Find the directional derivative of f at (1,0, 2) in the…

A: Solution

Q: 1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function…

A: The given function is;  f(x,y)=x2 Siny.

Q: If u = and Vf (-2, 5) = 3u, then the minimum value of the directional derivative Dy f (-2, 5) is…

A: We will use concept of minimum value of Directional Derivative and its direction

Q: 1. Find the gradient of the function f(x, y) = x² sin y.

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

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Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

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

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Q: Question 5 Suppose that f(x,y)= x^3 y^2. The directional derivative of f(x,y) in the directional (:…

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

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