Question

Find directional derivative of the function f(x, y, z) =
5*x ^{2}* + 2xy – 3

Answer #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〉.

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)

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

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 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

f(x,y,z) = xey+z.
(a) Find the gradient of f, ∇f.
(b) Find the directional derivative of f at the point (2, 1, 2)
in the direction of ? = 3? + 4?.

The electric potential (V) at a certain point in space is given
by: V(x, y, z) = 5x2-3xy+xyz
a) find the directional derivative of the potential at P(3,4,5)
in the direction of the vector v=i+j+k
b) calculate the gradient of the electric potential

find the directional derivative of f(x, y, z) = xy arctan (z) at
the point (1, 1, pi/4) in the direction <1, -1, 2>.

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