Exercise 3 . Let R be commutative zing ao+Q;X+.-+Qg ac"e R[xJ, The derivative f and %3D ('s defined ly the equolity fs =a,+2a #3qci+na,z . h- Prove thet (fog)'={'+, AgY=f'3+ fg , and m-1 %3D

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Chapter2: Second-order Linear Odes
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Modern Algebra:

Just prove the last one in red circle.

Esercise 3. commutative
Let R be a
ring
and
=00+Q,x+.-t@,ac" E R[xJ, The derivative f
%3D
('s
the equelity f's
defined ly -e,+20#3qcina,z
Prove thet (fag)'={'ag, G)=f'3+ fg , and
(G")' = mfm-"{' for m .
2.
17
Transcribed Image Text:Esercise 3. commutative Let R be a ring and =00+Q,x+.-t@,ac" E R[xJ, The derivative f %3D ('s the equelity f's defined ly -e,+20#3qcina,z Prove thet (fag)'={'ag, G)=f'3+ fg , and (G")' = mfm-"{' for m . 2. 17
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