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

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

the image of (6, 9) under a dilation is (4, 6). the scale factor is