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: f(x, y) = 3eª cos y, (a, b) = (0,7), and v = (3, 3). a. Calculate the directional derivative of f at…

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Q: Find the derivative of the vector function 7(t) = (e²¹, e-3¹, t). Find an equation of the line…

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Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

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Q: 2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P…

A: Tx,y=sin2x-y, P=-π3,π6,𝐐=0,0                                      P1  P2                𝐐1,…

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)…

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(3,…

A: Directional Derivative, Du f(x,y,z) = ∇f(x,y,z).u ; where , u is the unit vector  .

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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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: II. Consider the function g defined by 1 g(x, y) = cos (TX /y) + log3(x – y)" Do as indicated. 2.…

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

A: First find gradient and take magnitude for max rate of change