find the derivative

g(x)= ln x^(3/4)/((3x+5)^5)

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- Feb 3rd 2009, 03:25 PMSally_Mathfind the derivative
find the derivative

g(x)= ln x^(3/4)/((3x+5)^5) - Feb 3rd 2009, 03:46 PMskeeter
what an ugly function ...

$\displaystyle g(x) = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5}$

$\displaystyle g'(x) = \frac{3}{4} \cdot \frac{(3x+5)^5 \cdot \frac{1}{x} - \ln{x} \cdot 15(3x+5)^4}{(3x+5)^{10}}$

$\displaystyle g'(x) = \frac{3}{4} \cdot \frac{(3x+5) \cdot \frac{1}{x} - \ln{x} \cdot 15}{(3x+5)^6}$

$\displaystyle g'(x) = \frac{3(3x+5) - 15x\ln{x}}{4x(3x+5)^6}$ - Feb 3rd 2009, 03:54 PMSally_Math
- Feb 3rd 2009, 05:12 PMskeeter
- Feb 3rd 2009, 07:32 PMSally_Math
- Feb 4th 2009, 06:31 AMskeeter
then you should have used brackets to indicate ln[your

**expression**], like so ...

g(x)= ln[x^(3/4)/((3x+5)^5)]

or ...

$\displaystyle g(x) = \ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right]$

use the laws of logs to break up the expression into several logs, then find the derivative of each logarithmic term.

$\displaystyle

\ln\left[\frac{x^{\frac{3}{4}}}{(3x+5)^5}\right] = \frac{3}{4}\ln{x} - 5\ln(3x+5)$