- #1
kawsar
- 13
- 0
1. Find the directional derivative of the function f(x,y) = e[tex]^{xy}[/tex] at the point (-2,0) in the direction of the unit vector that makes an angle of [tex]\pi/3[/tex] with the positive x-axis
The vector to make into a unit vector is ([tex]\sqrt{3}[/tex],1) and e[tex]^{xy}[/tex] differentiated with respect to x and y is both e[tex]^{xy}[/tex] (I hope I'm right here!)
Made the unit vector ([tex]\frac{1}{2}[/tex]([tex]\sqrt{3}[/tex],1))
Use the dot product of (e[tex]^{xy}[/tex],e[tex]^{xy}[/tex]) and ([tex]\frac{1}{2}[/tex]([tex]\sqrt{3}[/tex],1))
Then use the coordinates from the point (-2,0) and to get [tex]\sqrt{3}[/tex]+1
Is this correct or have I missed a step or two?
Thanks!
The vector to make into a unit vector is ([tex]\sqrt{3}[/tex],1) and e[tex]^{xy}[/tex] differentiated with respect to x and y is both e[tex]^{xy}[/tex] (I hope I'm right here!)
Made the unit vector ([tex]\frac{1}{2}[/tex]([tex]\sqrt{3}[/tex],1))
Use the dot product of (e[tex]^{xy}[/tex],e[tex]^{xy}[/tex]) and ([tex]\frac{1}{2}[/tex]([tex]\sqrt{3}[/tex],1))
Then use the coordinates from the point (-2,0) and to get [tex]\sqrt{3}[/tex]+1
Is this correct or have I missed a step or two?
Thanks!