Question

fnd the directional derivative of the function given by:f(x,y,z)= x^2+xy+z at point (1,1,1) in direction of the vector a= i+2J+2k.

Answer 1

i found the gradient of 2x+y,x,2z

Answer 2

whats next

Answer 3

sorry, first we need our direction vector to be a unit vector, so it must be divided by its magnitude
can you do that?

Answer 4

no

Answer 5

the magnitude of the direction vector is its length
can you find that?

Answer 6

its 3 right?

Answer 7

3-dimensional pythagorean theorem\[\vec v=\langle a,b,c\rangle\implies\|\vec v\|=\sqrt{a^2+b^2+c^2}\]the double absolute value bars mean magnitude