Chapter 4: Partial Differentiation
Section 4.3: Chain Rule
Let Fx,y=frx,y,sx,y be defined by the composition of fr,s with r=x/y, s=y/x, for any sufficiently well-behaved function fr,s. Show that x⁢Fx+y⁢Fy=0.
x Fx+y Fy
=x fr rx+fs sx+y fr ry+fs sy
=x fr 1y+fs −yx2+y fr −xy2+fs 1x
=fr xy−fs yx+fr −xy+fs yx
=xy−xy fr+−yx+yx fs
Maple Solution - Interactive
Define rx,y and sx,y
Context Panel: Assign Name
Apply the chain rule to obtain x⁢Fx+y⁢Fy
Calculus palette: Partial-differential operator
Press the Enter key.
Context Panel: Simplify≻Simplify
x ∂∂ x fr,s+y ∂∂ y fr,s
Maple Solution - Coded
Implement the chain rule
Apply the simplify and diff commands.
x difffr,s,x +y difffr,s,y
simplifyx difffr,s,x +y difffr,s,y
<< Previous Example Section 4.3
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2023. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.
For more information on Maplesoft products and services, visit www.maplesoft.com
Download Help Document
What kind of issue would you like to report? (Optional)