GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Directional derivative of function along the line is the scalar value of derivative along the line. i.e. we have to calculate value of derivative of function in the direction of given line vector
$\nabla \mathit{f}=\stackrel{\wedge }{\mathit{ı}}\left(\frac{\partial \mathit{f}}{\mathit{d}\mathit{x}}\right)+\stackrel{\wedge }{\mathit{}}\left(\frac{\partial \mathit{f}}{\mathit{d}\mathit{y}}\right)$
$\nabla \mathit{f}=2\stackrel{\wedge }{\mathit{ı}}+2\stackrel{\wedge }{\mathit{}}$
Now, calculating the value of $\nabla \mathit{f}$ in $1\stackrel{\wedge }{\mathit{ı}}+1\stackrel{\wedge }{\mathit{j}}$
D.D of given function is $\left(2\stackrel{\wedge }{\mathit{ı}}+2\stackrel{\wedge }{}\right)\cdot -\frac{\left(\mathit{i}+\mathit{j}\right)}{\left|\mathit{i}+\mathit{j}\right|}==2\sqrt{2}$