use the chain rule to find the indicated partial derivatives

2个回答

  • 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

    ∂p/∂v=w ∂q/∂v=1 ∂r/∂v=u

    ∂p/∂w=v ∂q/∂w=u ∂r/∂w=1

    ∴when u=2 ,v=3 ,w=4 and p=14 q=11 r=10

    ∂N/∂p=-1/576 ∂N/∂q=1/24 ∂N/∂r=-25/576

    ∂p/∂u=1 ∂q/∂u=4 ∂r/∂u=3

    ∂p/∂v=4 ∂q/∂v=1 ∂r/∂v=2

    ∂p/∂w=3 ∂q/∂w=2 ∂r/∂w=1

    there for

    ∂N/∂u=(∂N/∂p)(∂p/∂u)+(∂N/∂q)(∂q/∂u)+(∂N/∂r)(∂r/∂u)=(-1/576)+(1/24)4+(-25/576)3=5/144

    ∂N/∂v=(∂N/∂p)(∂p/∂v)+(∂N/∂q)(∂q/∂v)+(∂N/∂r)(∂r/∂v)=(-1/576)4+(1/24)+(-25/5762=-15/288

    ∂N/∂w=(∂N/∂p)(∂p/∂w)+(∂N/∂q)(∂q/∂w)+(∂N/∂r)(∂r/∂w)=(-1/576)3+(1/24)2+(-25/576)=5/144