Consider the function g defined by g(x, y) = sin (T /Ty) + log3 (x – 3y) Do as indicated. 1. Determine dydx" 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) in the direction of the vector v = (1, 2). 3. In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the minimum directional derivative?

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

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 at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

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…

Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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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,…

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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 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…

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. 6. V12…

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Q: Calculate the derivative of the function. Then find the value of the derivative as specified. dr 6.…

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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: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

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