# Logarithmic Differentiation Simplifying

• Aug 28th 2012, 03:39 PM
Logarithmic Differentiation Simplifying
I've been given this problem and I've been working on it for a week on and off trying to figure out how to simplify it so it looks a bit cleaner. I can get the derivative without issue (I hope it's right) but my simplifying bag-of-tricks is not as developed as it should be.

Original question-- Use logarithmic differentiation to find the derivative:
$\displaystyle y=\frac{3^{-5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}$

$\displaystyle y'=\frac{3^{-5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}[-5ln(3)+\frac{8}{3(2x-3)}-\frac{14}{5(7x-5)}-\frac{9}{4(3x-7)}}]$

Is my instructor just trying to make me go mad or am I missing something? Trying to learn when to stop simplifying is difficult at times.
• Aug 28th 2012, 04:01 PM
Soroban
Re: Logarithmic Differentiation Simplifying

Quote:

I've been given this problem and I've been working on it for a week on and off
trying to figure out how to simplify it so it looks a bit cleaner.
I can get the derivative without issue (I hope it's right),
but my simplifying bag-of-tricks is not as developed as it should be.

Original question -- Use logarithmic differentiation to find the derivative:
. . $\displaystyle y\:=\:\frac{3^{\text{-}5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}$

$\displaystyle y'\:=\:\frac{3^{\text{-}5x}(2x-3)^\frac{4}{3}}{(7x-5)^\frac{2}{5}(3x-7)^\frac{3}{4}}\left[\text{-}5\ln(3)+\frac{8}{3(2x-3)}-\frac{14}{5(7x-5)}-\frac{9}{4(3x-7)}}\right]$

Is my instructor just trying to make me go mad or am I missing something?
Trying to learn when to stop simplifying is difficult at times.

. . I got the same answer.

If that is the book's answer (and I assume you didn't get it),
. . I need to see your work to make any comments.
• Aug 28th 2012, 04:07 PM
Re: Logarithmic Differentiation Simplifying
No that's my answer. I like to double check my work when I think I'm wrong. Thank you for the confidence.
• Aug 28th 2012, 06:42 PM
Prove It
Re: Logarithmic Differentiation Simplifying
If you like to double check your WORK, then you need to POST your work, not just the final answer...
• Aug 28th 2012, 07:06 PM