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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 directio

Home/Math/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 directio

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 directio

Question

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.

## Answers ( )

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