Question

If W = x^2 y^2 + xz, the directional derivative \( \frac{dW}{dl} \) in the direction 3 ax + 4 ay + 6 az at (1,2,0).

(a) 5

(b) 6

(c) 7

(d) 8

I got this question during a job interview.

The query is from Gradient of a Function and Conservative Field topic in division Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (b) 6

The best I can explain: First find the gradient of W which is (2xy^2+z) ax + 2yx^2 ay + x az

At (1,2,0) the gradient of W is 8 ax + 4 ay + 1 az

\(\frac{dW}{dl} = \) (Gradient of W ) . al

\( = (8,4,1) . \frac{(3,4,6)}{\sqrt{(9+16+36)}} \)

\(=5.88897 = 6.\)