Consider the function g defined by 1 g(x, y) = sin (TVry) + 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 of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

A:

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

A:

Q: f(x, y) = 5eª cos y, (a,b) = (0, 7), a. Calculate the directional derivative of f at the point (a,…

A:

Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

A:

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

A:

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

A:

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: 3. Find the directional derivative of f(x, y) = cos(3x+4y) at the point (7/6, π/6) along the…

A:

Q: Consider the function g defined by 1 g(x, y) = sin (TVry) + log3(x – 3y) Do as indicated. 1.…

A:

Q: Find the directional derivative of the function z(x, y) = e³tan(y) + (x + 1)²sin(2y) at the point…

A:

Q: Find the directional derivative of the function pez(x, y) = cos(2x) In (5y) + sin ¹(3x) (1-²)¹/2 at…

A:

Q: Calculate the directional derivative of f(x, y) = x²y in the direction of v = −3i+2j at the point P…

A:

Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

A:

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

A: