II. Consider the function g defined by 1 g(1, y) = cos (7I)+ log3(x – y) Do as indicated. 1. Determine dydx 2. Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vector v (1, 2). 3. In what direction does g have the maximum directional derivative at (z, y) = (4, 1)? What is the maximum directional derivative?

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

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

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

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Q: Pls help ASAP

A: Since, By Pythagorean identities will show that  Sin²θ + Cos²θ  = 1

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Q: II. Consider the function g defined by g(x, y) 3 = cos (Tx /y) + х — у Do as indicated. 1. Determine…

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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)…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum rate of change of a function f(x,y)�(�,�,�) occurs in the direction of the gradient…

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Q: Consider the function g defined by 1 g(x, y) = cos (TaV) + log3 (r-y) Do as indicated. 1. Determine…

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Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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