9.M(a, y, z)xyz xyz, P(2, -1, 1), u-10. f(x, y, z) y'e, P(0, 1, -1), u-11-17 Find the directional derivative of the function at the given(0,.-)4 1213, 13point in the direction of the vector v.(x. y) = e' sin y,(0, T/3),v= (-6, 8)X2 >(1, 2), v = (3,5)2. f(x, y)(2, 4),13. g(s, t) st,2i - jv14. g(u, v) = u?e , (3, 0), v 3i + 4j(1, 2, 3), v = (2, -1,2)15, f(x, y, z) = x'y + yz,WHG16. f(x, y, z) = xy tan z, (2, 1, 1), v= (1, 1, 1)17, h(r, s, t) = In (3r +6s +9t), (1, 1, 1),v = 4i + 12j + 6k18. Use the figure to estimate Du f(2, 2).у(2,2)Vf(2, 2)

Question
Asked Nov 22, 2019
19 views

#17 please 

9.M(a, y, z)xyz xyz, P(2, -1, 1), u-
10. f(x, y, z) y'e, P(0, 1, -1), u-
11-17 Find the directional derivative of the function at the given
(0,.-)
4 12
13, 13
point in the direction of the vector v.
(x. y) = e' sin y,
(0, T/3),
v= (-6, 8)
X
2 >
(1, 2), v = (3,5)
2. f(x, y)
(2, 4),
13. g(s, t) st,
2i - j
v
14. g(u, v) = u?e , (3, 0), v 3i + 4j
(1, 2, 3), v = (2, -1,2)
15, f(x, y, z) = x'y + yz,
WHG
16. f(x, y, z) = xy tan z, (2, 1, 1), v= (1, 1, 1)
17, h(r, s, t) = In (3r +6s +9t), (1, 1, 1),
v = 4i + 12j + 6k
18. Use the figure to estimate Du f(2, 2).
у
(2,2)
Vf(2, 2)
help_outline

Image Transcriptionclose

9.M(a, y, z)xyz xyz, P(2, -1, 1), u- 10. f(x, y, z) y'e, P(0, 1, -1), u- 11-17 Find the directional derivative of the function at the given (0,.-) 4 12 13, 13 point in the direction of the vector v. (x. y) = e' sin y, (0, T/3), v= (-6, 8) X 2 > (1, 2), v = (3,5) 2. f(x, y) (2, 4), 13. g(s, t) st, 2i - j v 14. g(u, v) = u?e , (3, 0), v 3i + 4j (1, 2, 3), v = (2, -1,2) 15, f(x, y, z) = x'y + yz, WHG 16. f(x, y, z) = xy tan z, (2, 1, 1), v= (1, 1, 1) 17, h(r, s, t) = In (3r +6s +9t), (1, 1, 1), v = 4i + 12j + 6k 18. Use the figure to estimate Du f(2, 2). у (2,2) Vf(2, 2)

fullscreen
check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Given:

help_outline

Image Transcriptionclose

h(r,s,t) In (3r +6s +9t), v=4î+12j+6k, (,1,1)

fullscreen
Step 2

If f is a differentiable function of x and y, then f(x ,y ,z) has a directional derivative in the direction of any unit vector v and

help_outline

Image Transcriptionclose

νπαί+αj+ q Dh (r, s,t) = h (r, s t) xα + h (7, s i) xα+h (7, s ) κα

fullscreen
Step 3

The directional derivative of h(r, s ,t) in the directi...

help_outline

Image Transcriptionclose

D,(r,st)=h, (r,5,t)xa +h (r,5,1) x a, + h (r, s, t) x a, h(r,s,t)=In(3r + 6s +91) d 3 (r,5,) = In(3r + 6s +91)) = (3r + 65 +9:) dr d 6 h (r,s,t)=(In(3r +65 +94)) = ds (3r+6s+9t) 9 (r,5,)=(In(3r+ 65 +94) = (3r+6s+9t)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add