Question

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

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

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the directional derivative of the function at the given point in the direction of the vector v.
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Transcript

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00:02 Resolution so we have the function a of r as t is equal to log 3r 6x 6s 90 and so d h over dr at the point 1 1 1 it's going to be equal to 3 over 3 plus 6 plus 9 which is equal to 1 over 6 so dh over ds at the point 1 1 1 similarly is equal to 6 over which is equal to 6 over 18 one third and the h over dt is going to be equal to one half so v is 4i 12j 6k so the length of v is equal to square root 12 square which is equal to 14 and so the normal…
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