Question

Find the directional derivative of the function at P in the direction of v. f(x, y)...

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)

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

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,

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
find the directional derivative of f (x, y) = x ^ 2 in the direction of...
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...
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...
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...
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...
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,...
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...
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...
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, ...
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 ,...
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 ) .
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT