Question

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→

Answer #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

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〉.

Given the function f(x, y, z) = (x2 + y2 +
z2 )−1/2
a) what is the gradient at the point (12,0,16)?
b) what is the directional derivative of f in the direction of
the vector u = (1,1,1) at the point (12,0,16)?

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 at the given
point in the direction of the vector v.
f(x,y,z)= x2y3+2xz+yz3
(-2,1,-1) v= <1,-2,2>
Use the chain rule to find dz/dt. z=sin(x,y) x= scos(t)
y=2t+s3

Find the directional derivative of the function at the given
point in the direction of the vector v.
f(x, y, z) = x2y + y2z, (2, 7, 9), v = (2,
−1, 2)
Dvf(2, 7, 9) =

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.

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).

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 17 minutes ago

asked 20 minutes ago

asked 25 minutes ago

asked 33 minutes ago

asked 34 minutes ago

asked 38 minutes ago

asked 54 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago