- #1

- 380

- 0

## Homework Statement

Find the Directional derivative of [tex]\varphi[/tex] = x

^{2}+siny-xz in the direction of

**i**+2

**j**-2

**k**at the point (1, [tex]\pi[/tex]/2 , -3)

## The Attempt at a Solution

**u**=

**i**+2

**j**-2

**k**

[tex]\left|[/tex]

**u**[tex]\left|[/tex] = [tex]\sqrt{1^2+2^2+(-2)^2}[/tex] = 3

[tex]\Rightarrow[/tex]

**u**[tex]\hat{}[/tex] = 1/3

**i**+2/3

**j**-2/3

**k**

[tex]\nabla[/tex][tex]\varphi[/tex] = (2x-z)

**i**+(Cos y)

**j**-x

**k**

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?