Find the directional derivative of f(x,y)=arctan(xy) at the point (-2,5) in the direction of maximum decrease.

What is the Domain and Range of f(x,y)=arctan(xy)?

Expert Solution

Colby Messinger answered 2 years ago

Find the directional derivative of f at the given point in the direction indicated by the...

Find the directional derivative of f at the given point in the direction indicated by the angle θ. f(x, y) = y cos(xy), (0, 1), θ = π/4 Duf(0, 1) =

The directional derivative of a function F(x,y) at a point P (1,-3) in the direction of...

The directional derivative of a function F(x,y) at a point P (1,-3) in the direction of the unit vector - 3/5 i + 4/5 j is equal to - 4 while its directional derivative at P in the direction of the unit vector (1/root5) i + (2/root5) j is equal to 0. Find the directional derivative of F(x,y ) at P in the direction from P(1,-3) towards the point Q(5,0).

Find the directional derivative of a funtion f(x,y,z)=x^2+e^xyz at point P(1,0,2) in the direction from P...

Find the directional derivative of a funtion f(x,y,z)=x^2+e^xyz at point P(1,0,2) in the direction from P to Q (1,1,1). is this max rate of change ?

A) Find the directional derivative of the function at the given point in the direction of...

A) Find the directional derivative of the function at the given point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v = <8, -6> Duf(5, 4) = B) Find the directional derivative, Duf, of the function at the given point in the direction of vector v. f(x, y) =ln(x2+y2), (4, 5), v = <-5, 4> Duf(4, 5) = C) Find the maximum rate of change of f at the given point and the direction...

Find the directional derivative of the function at the given point in the direction of the...

Find the directional derivative of the function at the given point in the direction of the vector v. ? = (2? + 3?)2, ? ⃑ = 1 2 ? ⃑+ √3 2 ? ⃑, (-1,1,1)

Given f(x,y) =(x3y- 2x2y) a) find the directional derivative of f(x,y) at (1, 2) in the...

Given f(x,y) =(x3y- 2x2y) a) find the directional derivative of f(x,y) at (1, 2) in the direction of <-3,4> b)find the maximum value of directional derivative at (2,4) and the direction in which this occurs

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of...

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of <3,-1>; c.the approximation for Δz when taking a Δs =0.05 step from (1,2) in direction of <3,-1>; d. the approximation to the maximum Δz possible when taking a Δs =0.05 step from (1,2).

Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...

Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point (−2, 1, −1) in the direction parallel to the line x = 3 + 4t, y = 2 − t, z = 3t. Answer: 58/√26 (b) Determine symmetric equations for the normal line to the level surface F(x, y, z)= −2 at the point (−1, 2, 1). Answer: x = −1 + 4t, y = 2 − 6t, z = 1 + 10t

1. (a) Find the directional derivative of f at (2,1) in the direction from (2,1) to...

1. (a) Find the directional derivative of f at (2,1) in the direction from (2,1) to (6,-2). Show your work clearly. (b) Find a unit vector u such that the directional derivative of f in the direction of u at (2,1) is zero. Show all work required to justify your answer.

Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector...

Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector v = 5i+2j−k. (a) Calculate the directional derivative of f at the point P in the direction of v. (b) Find the unit vector that points in the same direction as the max rate of change for f at the point P.

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