- #1
gtfitzpatrick
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- 0
Homework Statement
Find the Directional derivative of [tex]\varphi[/tex] = x2+siny-xz in the direction of i+2j-2k at the point (1, [tex]\pi[/tex]/2 , -3)
The Attempt at a Solution
u = i+2j-2k
[tex]\left|[/tex]u[tex]\left|[/tex] = [tex]\sqrt{1^2+2^2+(-2)^2}[/tex] = 3
[tex]\Rightarrow[/tex] u[tex]\hat{}[/tex] = 1/3i+2/3j-2/3k
[tex]\nabla[/tex][tex]\varphi[/tex] = (2x-z)i+(Cos y)j-xk
at the point (1, [tex]\pi[/tex]/2 , -3)
u[tex]\hat{}[/tex][tex]\nabla[/tex][tex]\varphi[/tex] = 5/3 + 0 +2/3 = 7/3
i think i have this right?