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in Mathematics by (19.2k points)

Calculate the directional derivative of the function 

f (x, y) = x − y/x + y 

at the point (x0 , y0 ) = (0, 1) 

(a) in the direction d = 2/2 i − 2/2 j and 

(b) the direction, in which the function is increasing most rapidly at the given point.

1 Answer

+1 vote
by (10.1k points)
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Best answer

We have 

The directional derivative in the direction d = 2/2 i − 2/2 j is given by

The direction, in which the function is increasing most rapidly is the direction of the gradient,

and the directional derivative in this direction is 

∇f (0, 1)· d = 2i · i = 2

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