Answer
$\dfrac{\partial N}{\partial u} =\dfrac{5}{144}$; and $\dfrac{\partial N}{\partial v} =\dfrac{-5}{96}$; and $\dfrac{\partial N}{\partial w} =\dfrac{5}{144}$
Work Step by Step
$\dfrac{\partial N}{\partial p} =\dfrac{(p+r)-(p+q)}{(p+r)^2}$
Plug the values $u=2;v=3; w=4$.
Here, we have $p=2+3 \times (4)=14; q=3+(2) \times (4)=11;r=4+(2)\times (3)=10$
$\dfrac{\partial N}{\partial p} =\dfrac{(14+10)-(14+11)}{14+10)^2}=\dfrac{-1}{(24)^2}$;
$\dfrac{\partial N}{\partial q} =\dfrac{(p+r)-0}{(p+r)^2}=\dfrac{1}{(p+r)}$
Plug the values $u=2;v=3; w=4$.
$\dfrac{\partial N}{\partial q} =\dfrac{1}{(14+10)}=\dfrac{1}{24}$;
Also, $\dfrac{\partial N}{\partial r} =\dfrac{0-(p+q)}{(p+r)^2}$
Plug the values $u=2;v=3; w=4$.
This gives: $\dfrac{\partial N}{\partial r} =\dfrac{-(14+11)}{(14+10)^2}=\dfrac{-25}{(24)^2}$
Our answers are: $\dfrac{\partial N}{\partial u} =\dfrac{5}{144}$; and $\dfrac{\partial N}{\partial v} =\dfrac{-5}{96}$; and $\dfrac{\partial N}{\partial w} =\dfrac{5}{144}$
