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Calculate the differential of the map

f:R^3 -> R^2 , (x ,y ,z)->(xy^{3}+ x^{2}z , x^{3}y^{2}z) 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.

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# Differential of a map (mathematical analysis)

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