Question

Let f(x y z)=x4y4+z5,

P=(4, 4, 1).

Calculate the directional derivative in the direction pointing to the origin. Remember to normalize the direction vector.

(Use symbolic notation and fractions where needed.)

Duf(4, 4, 1)

Answer #1

Let f(x y z)=x4y4+z5,
P=(4, 4, 1).
Calculate the directional derivative in the direction pointing
to the origin. Remember to normalize the direction vector.
(Use symbolic notation and fractions where needed.)
Duf(4, 4, 1)

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

Let f(x,y,z)=6xy−z^2, x=6rcos(θ), y=cos^2(θ), z=7r.
Use the Chain Rule to calculate the partial derivative.
(Use symbolic notation and fractions where needed. Express the
answer in terms of independent variables

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) =

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 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〉.

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?

a) evaluate the directional derivative of z=F(x,y) = sin(xy) in
the direction of u=(1,-1) at the point (0,pi/2)
b) Determine the slope of the tangent line
c) State the tangent vector

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.

Let f(x,y,z)=xy+z^3, x=r+s−8t, y=3rt, z=s^6.
Use the Chain Rule to calculate the partial derivatives.
(Use symbolic notation and fractions where needed. Express the
answer in terms of independent variables

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