1. ## find the derivative

find the derivative

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

2. Originally Posted by Sally_Math
find the derivative

g(x)= ln x^(3/4)/((3x+5)^5)
what an ugly function ...

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

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

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

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

3. Originally Posted by skeeter
what an ugly function ...

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

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

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

$g'(x) = \frac{3(3x+5) - 15x\ln{x}}{4x(3x+5)^6}$
thanks but is it the same for that the problem says ln((x^3/4)/(3x+5)^5)
Is this problem the same as the above

and thanks again

4. Originally Posted by Sally_Math
thanks but is it the same for that the problem says ln((x^3/4)/(3x+5)^5)
Is this problem the same as the above

and thanks again
you tell me ...

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

5. Originally Posted by skeeter
you tell me ...

is $\frac{\ln{x^{\frac{3}{4}}}}{(3x+5)^5} = \frac{3}{4} \cdot \frac{\ln{x}}{(3x+5)^5}$ ?
yes it is the same but I just wanted to ask bcz my eqn is ln(the eq.)

6. Originally Posted by Sally_Math
find the derivative

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

...

yes it is the same but I just wanted to ask bcz my eqn is ln(the eq.)
then you should have used brackets to indicate ln[your expression], like so ...

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

or ...

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

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

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