1. ## Natural logarithm question

Given the question 3(ln{sqrt(2x+3)})^2, find the derivative

I used the formula for chain rule and then did the necessary algebra and got this:

6(ln{sqrt(2x+3)})
2x+3

However the answer is listed as
3ln(2x+3)
2x+3

Can someone tell me where I made my error?

2. Hello,

There is no error

The thing is :

$\log(a^n)=n \log(a)$

Plus $\sqrt{b}=b^{\frac12}$

D'you see the trick ?

3. So the upper term can simplify like this:

6ln(2x+3)^1/2
= 1/2(6ln(2x+3))
=3ln(2x+3)

?

4. Exactly.