Is it true that int t dF/(d ln t) d ln t=in (dF)/(dt) dt

Kamila Frye

Kamila Frye

Answered question

2022-10-22

Is it true that t d F d ln t d ln t = d F d t d t

Answer & Explanation

Tiberlaue

Tiberlaue

Beginner2022-10-23Added 7 answers

A counter-example to the above formula is F ( t ) = ln t. Then
t d F d ln t d ( ln t ) = d t = t ,
but
d F d t d t = 1 t d t = ln t .
You can perform the u-substitution u=lnt to see that that
t d F d ln t d ( ln t )

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