use the chain rule to find the indicated partial derivatives N=(p+q)/(p+r),p=u+vw q=v+uw r=w+uv ;partial N/partial u ,partial N/partial v ,partial N/ partial w ,when u=2 ,v=3 ,w=4
问题描述：
use the chain rule to find the indicated partial derivatives
N=(p+q)/(p+r),p=u+vw q=v+uw r=w+uv ;
partial N/partial u ,partial N/partial v ,partial N/ partial w ,when u=2 ,v=3 ,w=4
答
N=(u+v+vw+uw)/(u+w+vw+uv)=(u+v)(1+w)/[(u+w)(1+v)]
N'u=(1+w)/(1+v)*[(u+w)-(u+v)]/(u+w)^2=(1+w)/(1+v)*(w-v)/(u+w)^2
N'v=(1+w)/(u+w)*[(1+v)-(u+v)]/(1+v)^2=(1+w)/(u+w)*(1-u)/(1+v)^2
N'w=(u+v)/(1+v)*[(u+w)-(1+w)]/(u+w)^2=(u+v)/(1+v)*(u-1)/(u+w)^2
当u=2, v=3,w=4时，代入得：
N'u=5/4*1/6^2=5/144
N'v=5/6*(-1)/4^2=-5/96
N'w=5/4*1/6^2=5/144
答
when u=2 ,v=3 ,w=4 then p=14 q=11 r=10∵∂N/∂p=1/(p+r)-(p+q)/(p+r)^2,∂N/∂q=1/(p+r),∂N/∂r=-(p+q)/(p+r)^2∂p/∂u=1 ∂q/∂u=w ∂r/∂u=v...