GATE IN 2005 | Vector Calculus Question 8 | Engineering Mathematics

A scalar field is given by $$f = {x^{2/3}} + {y^{2/3}},$$ where $$x$$ and $$y$$ are the Cartesian coordinates. The derivative of $$'f'$$ along the line $$y=x$$ directed away from the origin at the point $$(8, 8)$$ is

$${{\sqrt 2 } \over 3}$$

$${{\sqrt 3 } \over 2}$$

$${2 \over {\sqrt 3 }}$$

$${3 \over {\sqrt 2 }}$$

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Engineering Mathematics