# 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)

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19 views help_outlineImage Transcriptionclose9.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
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Step 1

Given:

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_outlineImage Transcriptioncloseνπαί+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_outlineImage TranscriptioncloseD,(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

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