Directional derivative

  • #1

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?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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I think you have it right.
 
  • #3
thanks a mill
 

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