(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Directional derivative of [tex]\varphi[/tex] = x^{2}+siny-xz in the direction ofi+2j-2kat the point (1, [tex]\pi[/tex]/2 , -3)

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?

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# Directional derivative

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