Find the directional derivative of function f(x y)=x°e' at the point (1,1) and direction of vector v=2i.

Q: find the gradient of the function and the maximum value of th directional derivative at the given…

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Q: (a) Find the directional derivative of f (x,y) = In(xy) at (-) in the direction of (1,1).

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

Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: What is the gradient of a function f(x, y) and why might we want to calculate it? How does it relate…

A: Properties of gradient of function

Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

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Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: Find the derivative of the vector function below r(x ) = sin²(sec.x 2)i +csc³(Vx ² +1) j +8tan(x -k

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Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

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Q: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction…

A: Firstly, we calculate unit vector in direction of vector u.

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

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Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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

A: Given function, f(x,y)=y2 ln x Point 1,2 and vector u=3,4 The unit vector of u is…

Q: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

A: Solution a: Given function is f(x, y)=xy+y Now gradient of the function is ∆f(x, y)=∂f∂x, ∂f∂y⇒∆f(x,…

Q: Find the unit vector towards the tangent of the curve y = x at x =1

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Q: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

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: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

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

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Q: Find the directional derivative of the function f(x, y) =1+5zj at the point (5, 1) in the direction…

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Q: Find the directional derivative of the function f(x, y) = x² + y³ at the point (2, 1) in the…

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Q: Find the derivative of the vector function below r(x ) = sin°(secx ²)i +csc°(Vx² +1)j +8tan(x -)

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Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: Find the directional derivative of f(x, y, z) = xy + z 3 at the pointP = (3, -2, -1) in the…

A: fx, y, z=xy+z3,  P=3, -2, -1. Now, ∂f∂x=y·1+0=y∂f∂y=x·1+0=x∂f∂z=0+3z2=3z2 Now, ∇fx, y, z=∂f∂x, ∂f∂y,…

Q: The directional derivative of xy f(x, y) = x + y) at (1, 1) in the direction of the unit vector at…

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Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: Find the directional derivative of the given function at the given point in the direction of the…

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

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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 unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: Find the derivative of the vector function r(t) = (tan t, sec t,). %3D t2

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Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function fx,y,z=x3-xy2-z at the point p02,1,0 in the direction of vector v=2i-3j+6k. Find…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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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 directional derivative of the function f(x, y) = In(x + y²) at the point (1, - 1) in the…

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Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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Q: Find the directional derivative of f(x,y)=sin(2x−2y) at the point (π/2,π/6)in the direction of the…

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