Question

F(x, y, z) = x2yz − xyz3, p(2, −1, 1), u = 0, 4 5 , − 3 5 (a) find the gradient of f.

Answer 1

The "gradient of F" here is the following sum:

(partial of F with respect to x)i + (partial of F with respect to y)j + (partial of F with respect to z)k.

Please, use "^" to denote exponentiation:  F(x, y, z) = x2yz − xyz3 should be presented as F(x, y, z) = x^2yz − xyz^3.

The partial of F with respect to x is 2xyz.  That with respect to y is 
x^2z.  That with respect to z is -3xyz^2.

Thus, your gradient is 

G(x,y,z) = 2xyz i + x^2z j + -3xyz^2 k.