Find the directional derivative of f ( x , y , z ) = x y + z 3 f(x, y,z)=xy+z3 at the point P = ( 4 , − 7 , − 2 ) P=(4,−7,−2) in the direction pointing to the origin.

has gradient

The derivative of at in the direction of a vector is

In this case, is the vector pointing from to the origin, which is

and has norm

Then the derivative of at in the direction of is

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)

step-by-step explanation:

cats