Obtain the directional derivative of f (x, y) = 2root (x) -y ^ 3 at the point (1,3) in the direction towards the point (3,1), select the correct option.

Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: The objective is to write what is the gradient vector of a differentiable function ƒ(x, y) and how…

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

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Q: Write down the the definition (in terms of limits) of the directional derivative and use it to…

A: We have to write down the definition of the directional derivative and also find the directional…

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: 8. Find directional derivative of function z = xey at point P(1,0) in the direction from pointP(1,0)…

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Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

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Q: Find the directional derivative of f(x, y) = 3x² - 2y² at point ,0) to point 3 (-2-1,0) 0(0,1). in…

A: Let's find directional derivative.

Q: What is the definition of the directional derivative for afunction of two variables, f (x, y)? Be…

A: Definition of directional derivative of function of two variable.

Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = ry. The directional…

A: Find the directional derivative of the function

Q: Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

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Q: Find the direction 0 in which the directional derivative of the function x + y f(x, y) = 2(x + y) -…

A: Given that: f(x, y)=2(x+y)-x+yxy

Q: What is the directional derivative of the function f(x.y)-2xy-3y at point p.- (5,5) in the direction…

A: To find: The directional derivative of the function f(x,y)=2xy-3y2 at point P=(5,5) in the direction…

Q: Find the directional derivative of f(x, y) = direction of Q(2,-2). NOTE: Enter the exact answer. √2…

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the…

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: Find the direction for which directional derivative of f (x,y) = 3x² – 4xy + 2y² +29 at (-2,3) is…

A: Formula: The maximum directional derivative of f(x, y) at (a, b) is given by ∇f(a, b) and direction…

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

A: Given:        fx,y=4yx   at point 4,5     The rate of change of f is     ∇fx,y=∂f∂x,∂f∂y…

Q: What is the definition of the directional derivative for afunction of three variables, f (x, y, z)?…

A: The directional derivative of f(x,y,z) in the direction of the unit vector u=⟨a,b,c⟩ is given by,…

Q: Use directional derivative definition to find derivative of V3. f(x, y) = x² + y² at the direction…

A: Consider the given function as fx,y=x2+y2

Q: Find the directional derivatives of Ø = x2yz + 4xz2 at ( 1, -2, -1) in direction 2ax – ay – 2az.

A: Answer is in step 2.

Q: Find the gradient of the function at the given point. Function Point (7,4) f(x, y) = Vf(7, 4) = x +…

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Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…

A: Here is the solution of the given problem. Unit Direction:

Q: Find the directional derivative of f(x, y) = 5e-y at (-1, 1) in the direction of (-4,3). %3D

A: The directional derivative is the dot product of the gradient at the given point and the normalized…

Q: Suppose that f(x, y) (x, y) (,5) = xy. Find the directional derivative of f(r, y) in the direction…

A: Given

Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

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Q: Suppose that f(r, y) the point (r, y) 3 (6, ry. The directional.derivative of f(z, y) in the…

A: Given:  fx, y=xy To Find:  To find the direction derivative of fx, y at the point x, y=6, -4, in the…

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional and at the…

A: we will find the directional derivative

Q: Suppose that f(x, y) = x*y². The directional derivative of f(x, y) in the directional and at the…

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Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

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

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (- 3, 1) and…

A: First find gradient at point and take dot product with unit vector

Q: Find the directional derivative of f(x, y) at the point (9,0) in the direction indi- -8y xe cated by…

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Q: 3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the…

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Q: Find the directional derivative of f(x, y) = 3x² - y² + 5xy at (2,-1) in the direction of -3i - 4j.

A: given function f(x,y)=3x2-y2+5xy given point (2, -1) given direction u→=-3i-4j We have to find the…

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (-4, -4) and the direction in…

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Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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Q: Find the directional derivative of f(x,y) = sin(x+2y) at the point (1, -3) in the direction θ=3π/4

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Q: compute th directional derivative of f(x,y) at point P in the direction of the point Q .

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Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = a°y?. The directional…

A: Given function is fx,y=x3y2 We have to find the directional derivative of fx,y in the direction of…

Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: , (a) Find the directional derivative of at (-2,1) in the direction u = ?-j. X.

A: Since you have asked a different question. I am answering the first one. Please post the question…

Q: 15 /(х. у) 2гу-Зх, Р % (2, 1), - (3,2)

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) + y2 + z2 (3, 7, 2)…

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Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Find the maximum value of the directional derivative at the point (3, 4) of the function x+y f(x.y)=…

A: The given function is fx,y=x+yy+6  and the point is 3,4. To find the maximum value of the…

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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