Search
Duplicate

데코수학/ 벡터미적분학/ 다변수 실함수의 미분 (연쇄법칙)

(유튜브 동영상인데 현재는 삭제되어서 내용만 남김)

개념

•
f,gf, g: 미분가능이면, ⇒f+g,α⋅f,f⋅g\Rightarrow f + g, \alpha \cdot f, f \cdot g 도 미분가능
•
연쇄법칙
◦
f(x1,x2,...,xn),xif(x_{1}, x_{2}, ... , x_{n}), x_{i} 들이 t1,t2,...,tnt_{1}, t_{2}, ... , t_{n} 에 대한 함수이면
▪
Δf≈∂f∂x1Δx1+∂f∂x2Δx2+∂f∂xnΔxn\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}
▪
ΔfΔtk≈∂f∂x1Δx1Δtk+∂f∂x2Δx2Δtk+∂f∂xnΔxnΔtk{\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}}
▪
∂f∂tk=∂f∂x1∂x1∂tk+∂f∂x2∂x2∂tk+∂f∂xn∂xn∂tk{\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}}
Made with