Derivative of a natural log: Find dR/dS for R = k ln(S/So)

[Linty Fresh]

Given the equation:

R = k * ln(S/So) where R is the response, S is the stimulus, and So is the lowest level of detectable stimulus, find dR/dS

Is dR/dS the same as R'? If so:

ln(S/So) = (ln S - ln So)

R = k*(ln S - ln So)

R' = uv' + vu' = (k)(1/S - 1/So) + (ln S - ln So)(0)

= k(1/S - 1/So)

And it's about here that I realize I have absolutely no idea what I'm doing! Anyone have any pointers? Many thanks!

 

[stapel]

As far as the function R(S) is concerned, S₀ is just some number. (It is a fixed constant, right?) This makes ln(S₀) just a constant.

What is the derivative of a constant? :wink:

Eliz.

 

[Linty Fresh]

Ahhh, didn't realize it was a constant. That makes sense, thanks!