Question

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)

Answer #1

we have

now,

so the gradient of f is,

gradient at point (8, 5) we can say that,

the unit vector in direction of v = 2(i+j) = (2, 2) is,

hence the directional derivative of f(x,y) is,

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

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 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

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?

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.

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) =
tan−1(xy) at the point (1, 3) in the direction of the unit vector
parallel to the vector v = 4i + j.

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 ) .

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