Question

find the directional derivative of f (x, y) = x ^ 2 in the
direction of v = i-j for the point (-1,2).

Answer #1

Find the directional derivative of the function at P in the
direction of v. f(x, y) = x3 − y3, P(8, 5), v = 2 2 (i + j)

Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the
directional derivative of f 1+x^2+y^2 at the point (10, 6) in the
direction of: (a) u = 3 i − 2 j (b) v = −i + 4 j

Calculate the directional derivative at point p in the direction a.
1) f (x, y) = (x ^ 2)*(y); p = (1,2); a ⃗ = 3i-4j
2) f (x, y, z) = (x ^ 3)*(y) - (y ^ 2)*(z ^ 2); p = (- 2,1,3); a ⃗ = i-2j + 2k

Find the gradient ∇f and the directional derivative at the point
P (1,−1,2) in the direction a = (2,−1,1) for the function f (x,y,z)
= x^3z − y(x^2) + z^2. In which direction is the directional
derivative at P decreasing most rapidly and what is its value?

Find the directional derivative of the function at the given
point, in the
vector direction v
1- f(x, y) = ln(x^2 + y^2 ), (2, I), v = ( - 1, 2)
2- g(r, 0) = e^-r sin ø, (0, ∏/ 3), v = 3 i - 2 j

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...

Find directional derivative of the function f(x, y, z) =
5x2 + 2xy – 3y2z at
P(1, 0, 1) in the direction v = i +
j – k .

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 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 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.

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