Given y(x) = A*exp(x+c). I'm converting the y-axis into a log-scale. Then I calculate the slope at a certain point. Am I'm allowed to re-transform this value dy(x)/dx? Hence: exp(dy(x)/dx)?

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    $\begingroup$ Presuming $A$ to be positive, it seems odd to have a multiplicative constant term $A$ and an additive term in the $\exp$, since they serve the same function. $A\exp(x+c) = Ae^c \exp(x) = A^* \exp(x)$ (or if you prefer, $A\exp(x+c) = e^{x + c+\log(A)}=e^{x + c^*}$). $\endgroup$ – Glen_b Jan 11 '19 at 11:31
  • $\begingroup$ Correct, didn't have these rules in my mind anymore. Thank you! $\endgroup$ – Ben Jan 11 '19 at 16:12

Exponentiating the derivative of the log is not the same as the derivative of the original function ($\log$ and $\exp$ aren't linear operators):

$$\frac{d}{dx} Ae^{x+c} = Ae^c \frac{d}{dx} e^x = Ae^{x+c}$$

If you take logs of $Ae^{x+c}$ you get $\log A + c + x$, and so the slope on the log scale is 1. If you exponentiate that you get $e$. Clearly that's not going to be correct; the slope isn't constant.

  • $\begingroup$ Thank you! I've a similar question: I'm interested in x(f(x)=1)=? and I perform a logarithmical transformation to get a better regression => log(x(f(x)=1)=log(?)? Then I can make a exp-transformation on this regressed x-value. And when I'm interested in the slope at this x-value, am I'm forced to apply the derivative on the log-transformation or am I'm also allowed to do it without? Hope that is understandable? $\endgroup$ – Ben Jan 12 '19 at 11:32
  • $\begingroup$ Sorry I couldn't follow that at all. If you have a new question and can ask it in a clearer way, you could post it $\endgroup$ – Glen_b Jan 12 '19 at 15:23

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