Question

Find the directional derivative of the function f (x, y) = tan−1(xy) at the point (1, 3) in the direction of the unit vector parallel to the vector v = 4i + j.

Answer #1

1. Let f(x, y) = 2x + xy^2 , x, y ∈ R.
(a) Find the directional derivative Duf of f at the point (1, 2)
in the direction of the vector →v = 3→i + 4→j .
(b) Find the maximum directional derivative of f and a unit
vector corresponding to the maximum directional derivative at the
point (1, 2).
(c) Find the minimum directional derivative and a unit vector in
the direction of maximal decrease at the point...

For the function f(x, y)=ln(1+xy)
a.Find the value of the directional derivative of f at the point
(-1, -2) in the direction <3,4>.
b.Find the unit vector that gives the direction of steepest
increase of f at the point (2,3).

let
f(x,y) = xe^(xy)
Find the directional derivative of f at point (2,0) in the
direction of vector <-6,8>. Find the maximum rate of change
of f at point (2,0) and the direction in which it occurs.

16.
a. Find the directional derivative of f (x, y) = xy at P0 = (1,
2) in the direction of v = 〈3, 4〉.
b. Find the equation of the tangent plane to the level surface
xy2 + y3z4 = 2 at the point (1, 1, 1).
c. Determine all critical points of the function f(x,y)=y3
+3x2y−6x2 −6y2 +2.

the function f(x; y) = xye^x-y, at the point (2; 2) (1)find the
gradient. (2) find the directional derivative in the direction of
the vector 3i - j. (3)find the direction of which unit vector is
the rate of increase maximum? What is the maxi- mum rate of
increase? (4)find the direction of which unit vector(s) is the
directional derivative zero?

Find the directional derivative of the function
f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the
vector < - 2 ,2>.
b) Also find the maximum rate of change of f at the given
point and the unit vector of the direction in which the maximum
occurs.

Find the directional derivative of the function
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→

Find the value of the directional
derivative of the function w = f ( x , y , z ) = 2 x y + 3 y z
- 4 x z
in the direction of the vector v =
< 1 , -1 , 1 > at the point P ( 1 , 1 , 1 ) .

Find the directional derivative of the function f(x, y, z) = 4xy
+ xy3z − x z at the point P = (2, 0, −1) in the direction of the
vector v = 〈2, 9, −6〉.

Compute the directional derivative of f at the given
point in the direction of the indicated vector.
f(x, y) =
e4x2 − y, (1, 4),
u in the direction of −4i −
j
Duf(1, 4) =

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 30 minutes ago

asked 35 minutes ago

asked 37 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago