Taking a logarithmic derivative of a function I have the following expression: log &#x2061;<!

veirarer 2022-06-27 Answered
Taking a logarithmic derivative of a function
I have the following expression:
log ( 1 r r s )
which I would like to take the following derivative of (and where r s is a constant):
d ( log ( 1 r r s ) ) d log ( r )
What kind of strategies could I employ to find a solution?
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Answers (2)

Odin Jacobson
Answered 2022-06-28 Author has 17 answers
let t = log r then e t = r substituting in your expression you have to find
d d t log ( 1 e t r n )
after differentiating retain the value of r

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Petrovcic2x
Answered 2022-06-29 Author has 11 answers
Consider that you have log(u). Then apply d(log(u))/du = 1 / u. Now, since you want, I guess, the derivative with respect to "r" and since u = 1 - r / rs, then du/dr = - 1 / rs and so,
d(log[1 - r / rs])/dr = d(Log(u))/du * du/dr = 1 / (r - rs).

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