데코수학/ 다변수 실함수의 미분 (연쇄법칙)

개념

  • f, g : 미분가능이면, \Rightarrow f + g, \alpha \cdot f, f \cdot g 도 미분가능
  • 연쇄법칙
    • f(x_{1}, x_{2}, ... , x_{n}), x_{i} 들이 t_{1}, t_{2}, ... , t_{n} 에 대한 함수이면
      • \Delta f \approx {\partial f \over \partial x_{1}} \Delta x_{1} + {\partial f \over \partial x_{2}} \Delta x_{2} + {\partial f \over \partial x_{n}} \Delta x_{n}
      • {\Delta f \over \Delta t_{k}} \approx {\partial f \over \partial x_{1}} {\Delta x_{1} \over \Delta t_{k}} + {\partial f \over \partial x_{2}} {\Delta x_{2} \over \Delta t_{k}} +  {\partial f \over \partial x_{n}} {\Delta x_{n} \over \Delta t_{k}}
      • {\partial f \over \partial t_{k}} = {\partial f \over \partial x_{1}} {\partial x_{1} \over \partial t_{k}} + {\partial f \over \partial x_{2}} {\partial x_{2} \over \partial t_{k}} +  {\partial f \over \partial x_{n}} {\partial x_{n} \over \partial t_{k}}
[ssba]

The author

지성을 추구하는 디자이너/ suyeongpark@abyne.com

댓글 남기기

This site uses Akismet to reduce spam. Learn how your comment data is processed.