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
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