Let-f-R-3-R-be-define-by-f-x-y-z-2x-2-y-6xy-z-3-3z-calculate-the-directional-deriva-tive-of-the-vector-u-2-1-3-help-

Question Number 192398 by Mastermind last updated on 16/May/23

Let f : R^{3} \to R be define by

f (x, y, z) = {2 x}^{2} - y + 6 xy - z^{3} + 3 z .

calculate the directional deriva -

tive of the vector u = (2, 1, - 3)

help!

Answered by aleks041103 last updated on 21/May/23

(u \cdot ▽) f = 2 \partial_{x} f + \partial_{y} f - 3 \partial_{z} f =

= 2 (4 x + 6 y) + (- 1 + 6 x) - 3 (- 3 z^{2} + 3) =

= 8 x + 12 y - 1 + 6 x + 9 z^{2} - 9 =

= 14 x + 12 y + 9 z^{2} - 10