Answer
$\dfrac{\partial N}{\partial u} =\dfrac{5}{144} \\ \dfrac{\partial N}{\partial v} =\dfrac{-5}{96} \\ \dfrac{\partial N}{\partial w} =\dfrac{5}{144}$
Work Step by Step
We have $p=2+3(4)=14; q=3+(2)(4)=11;r=4+(2)(3)=10$
Now, $\dfrac{\partial N}{\partial p} =\dfrac{(p+r)-(p+q)}{(p+r)^2}$ and $\dfrac{\partial N}{\partial q} =\dfrac{(p+r)-0}{(p+r)^2}=\dfrac{1}{(p+r)}$ and $\dfrac{\partial N}{\partial r} =\dfrac{0-(p+q)}{(p+r)^2}$
For $u=2;v=3; w=4$:
$\dfrac{\partial N}{\partial p} =\dfrac{-1}{(24)^2}$;
$\dfrac{\partial N}{\partial q} =\dfrac{(14+10)-0}{(14+10)^2}=\dfrac{1}{24}$
$\dfrac{\partial N}{\partial r} =\dfrac{0-(14+11)}{(14+10)^2}=\dfrac{-25}{(24)^2}$
