Directional derivatives, SIMPLE

[pleasehelpme6]

f(x, y, z) = xe^y + ye^z + ze^x, at (0, 0, 0),

directional vector v = <-2, 0, 5>

i solved for gradient f = (e^y + ze^x, xe^y + e^z, ye^z + e^x), at f(0,0,0) to be...

gradient f = (1,1,1)

this would make the answer just be -2 + 0 + 5 = 3
but this isn't right.

can someone show me what i did wrong?

 

[pleasehelpme6]

please.

 

[fzero]

The directional derivative involves the unit vector in the direction of v, not v itself. Find the unit vector u = v/|v| and use that in your calculation.

 

[pleasehelpme6]

thank you! that makes a lot of sense