How to take derivative with respect to logarithmic function

Question

I have a function g as a function of x; i want to take derivative of g with respect to ln x, i.e. dg/d ln x where g= ax^2/(1+ax^2/r^2)

Is this a question about math (or maths), or the software Mathematica? — evanb, Jan 17 '15 at 07:13
Please do clarify if this is to be solved using Wolfram Mathematica or if I should migrate this question to [Math.SE]. — Mr.Wizard, Jan 17 '15 at 14:52

zjx1805 · Answer 1 · 2015-01-17T09:23:23.803

3

You have to do a transformation first:

$ \frac{d \textrm{ln(x)}}{d\textrm{x}}=\frac{1}{x} \Rightarrow d\textrm{ln(x)}=\frac{d\textrm{x}}{x}$

Therefore,

$ \frac{d\textrm{g}}{d\textrm{ln(x)}}=\frac{d\textrm{g}}{d\textrm{x}}\cdot x$

Then you can proceed as normal. Hope it helps.

edited Jan 17 '15 at 09:23

answered Jan 17 '15 at 08:57

zjx1805

Hi ! Unfortunately this answer does not rely on Mathematica's capabilities and as such is more of a comment. – Sektor Jan 17 '15 at 09:23
I think he is trying to solve this problem in Mathematica, but the derivative function in Mathematica doesn't support directly inputing D[g[x],ln(x)] – zjx1805 Jan 17 '15 at 09:54

score 1 · Answer 2 · answered Jan 17 '15 at 13:23

1

Chain rule. This syntax form is easily generalized.

D[g,x]/D[Log[x],x]

answered Jan 17 '15 at 13:23

Craig Carter

Your function g is not a function of x. – Sektor Jan 17 '15 at 13:52
Ummmm... But the poster's was. How about D[function[x],x]/D[anotherFunction[x],x]? – Craig Carter Jan 18 '15 at 01:05

2 Answers2