1. ## Differentiating ln

I expect this to be a simple question. However, I have never met this type of question before and have some doubts on differentiating such functions..

Differentiate $\displaystyle y=\frac{lnx}{2x+3}$

2. Originally Posted by Punch
I expect this to be a simple question. However, I have never met this type of question before and have some doubts on differentiating such functions..

Differentiate $\displaystyle y=\frac{lnx}{2x+3}$
Yes, it is a simple question. First, it is a quotient so you need the quotient rule:
$\displaystyle \left(\frac{f(x)}{g(x)}\right)'= \frac{f'(x)g(x)- f(x)g'(x)}{g^2(x)}$.

You will also need to know that if f(x)= ln(x) then f'(x)= 1/x and if g(x)= 2x+3, then g'= 2.

3. Hi, I understood everything except for f(x)= ln(x) then f'(x)= 1/x

4. Originally Posted by Punch
Hi, I understood everything except for f(x)= ln(x) then f'(x)= 1/x
here is a definition of the natural log function ...

$\displaystyle \ln{x} = \int_1^x \frac{1}{t} \, dt$

using the FTC ...

$\displaystyle \frac{d}{dx} \left[\ln{x} = \int_1^x \frac{1}{t} \, dt\right]$

$\displaystyle \frac{d}{dx} \ln{x} = \frac{1}{x}$