Monday, July 30, 2018

10:06 AM

Differential Approximation to \Delta F If 𝛥𝐹 = 𝑓(𝑥) − 𝑓(﷐𝑥﷮0﷯) then Δ𝑓 ≅ ﷐﷐𝑓﷮′﷯﷐﷐𝑥﷮0﷯﷯﷮Δ𝑥﷯ Define function Calculate partial derivative Two varianle function roles What about for z=f(x,y) If F=F(x,y), x=x(t), y=y(t) Then... dF/dt = DF/Dx dx/dt + Df/Dy dy/dt dF/dt = sum of the products of the derivatives along the branches If z=F(x,y) = x^2 y + 3xy^4 and x=e^t, y=sin(t) , then use the chain rule to find dz/dt X ----------\ / dz/dx \ dx/dt Z t \ dz/dy / dy/dt y ----------/ dz/dt = Dz/Dx dx/dt + Dz/Dy dy/dt z = x^2 y + 3xy^4 x = e^t y = sin(t) Dz/Dx = 2xy + 3y^4 Dz/Dy = x^2 + 3x * 4y^3 dx/dt = e^t dy/dt = cos(t) dz/dt = Dz/Dx dx/dt + Dz/Dy dy/dt … Chain Rule Formula 2 If F is a function of x and y and x=x(s,t) and y=y(s,t) then... DF/Dt = Df/Dx Dx/Dt + DF/Dy Dy/Dt
DF/Dt = Df/Dx Dx/Dt + DF/Dy Dy/Dt To get Df/Ds = DF/Dx Dx/Ds + Df/Dy Dy/Ds Chain Rule Formula 3 If 𝐹=𝐹(𝑢) and 𝑢=𝑢﷐𝑥,𝑦﷯ … Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings Ink Drawings

 

Created with Microsoft OneNote 2016.