# Derivatives of natural logarithmic functions

## Main Question or Discussion Point

f(x) = ln (12x-5/9x-2)

f'(x) = (4/3) (1/ln10)(9x-2/12x-5)

Is this correct??

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CompuChip
Homework Helper
Instead of ln(10) you should put ln(base of the logarithm), in this case; ln(e) = 1. When deriving log(x) (base 10), you can rewrite to ln(x)/ln(10). ln(10) is just a constant, so the derivative of this is 1/ln(10) * 1/x.

Also, I think you didn't do the chain rule quite right.

Then, is this
f(x) = ln (12x-5)
g(x) = ln (9x-2)
f'(x) = 12/12x-5
g'(x) = 9/9x-2

Correct??

Is this correct:

(12/12(ln9x-2)-5)-(9/9x-2)

Last edited:
Defennder
Homework Helper
fr33pl4gu3 said:
(12/12(ln9x-2)-5)-(9/9x-2)
This should not have ln inside. What is d/dx ln(12x-5) ? You've got it from above, just put it into this one.

CompuChip