Differential of a map (mathematical analysis)

[Laney5]

Im not sure if this is the right section to post this question..

Calculate the differential of the map
f:R^3 -> R^2 , (x ,y ,z)->(xy³ + x²z , x³y²z) at (1 ,2 ,3) in the direction (1 ,-1 , 4)

I know how to get the differential of the map (finding the jacobian matrix) but the only part i am not sure about is the 'in the direction' part. how do i use (1 ,-1 ,4) in trying to get the answer?
thanks.

 

[Tac-Tics]

Im not sure if this is the right section to post this question..

Calculate the differential of the map
f:R^3 -> R^2 , (x ,y ,z)->(xy³ + x²z , x³y²z) at (1 ,2 ,3) in the direction (1 ,-1 , 4)

I know how to get the differential of the map (finding the jacobian matrix) but the only part i am not sure about is the 'in the direction' part. how do i use (1 ,-1 ,4) in trying to get the answer?
thanks.

Why not parametrize the function? Let g(t) = f(tv) where v is (1, -1, 4) / length(1,-1,4). This function g(t) then represents the value of f when you walk a distance t in the direction (1,-1,4).