What is the appropriate way to simplify such an expression. i am unsure of how...

William Cleghorn

William Cleghorn

Answered

2022-01-06

What is the appropriate way to simplify such an expression. i am unsure of how to use the series i know to apply to this situation
L=0MsLL2

Answer & Explanation

aquariump9

aquariump9

Expert

2022-01-07Added 40 answers

Write : L2=L(L1)+L and use derivative. For L2:
L2sL=s2L(L1)sL2+sLsL1=s2(sL)+s(sL)
We get:
L=0ML2sL=02+12s+s2(L=2MsL)+s(L=2MsL)
Neunassauk8

Neunassauk8

Expert

2022-01-08Added 30 answers

Try to make the inner expression look like a derivative:
L=0M(LsL1)sL=sL=0M(dssL)L
=sdsL=0MsLL
=sdsL=0M(LsL1)s
=sds(sL=0M(LsL1))
=sds(sL=0MdssL)
=sds(sdsL=0MsL)
=sds(sdssM+11s1)
Now just take it from here, simplifying from the inside out.
karton

karton

Expert

2022-01-11Added 439 answers

Rewrite L2=L(L1)+L. Then,
L=0ML2sL=L=0ML(L1)sL+L=0MLsL
=s2d2ds2L=0MsL+sddsL=0MsL

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