The directional derivative of the function f(x, y) = x²

The directional derivative of the function f(x, y) = x² + y² along a line directed from (0, 0) to (1, 1), evaluated at the point x = 1, y = 1 is

Directional derivative = ∇f.	a
	\|a\|

∇f =	δx²	̂i +	δy²	̂j
	δx		δy

= 2xî + 2yĵ
a = line joining (0,0) and (1,1)
1î + 1ĵ
a = î + ĵ

Directional derivative =	(2xî + 2yĵ)(î + ĵ)
	√2

=	2x + 2y
	√2

Directional derivative at (1,1) =	2 + 2	= 2√2
	√2