Find derivative of y. y= ln (1 + √x) / (x^3)

1. Oct 24, 2012

HellRyu

1. The problem statement, all variables and given/known data

Hi guys, I've got :

$$y= ln ( (1 + √x) / x^{3})$$

2. The attempt at a solution
I honestly don't know where to go from here, I tried getting the ln of each of them.

$$y = ln 1 +ln√x - ln x^{3}$$

Am I doing it write? If not, how am I suppose to work this problem out? If so, where do I go from here?

2. Oct 24, 2012

MarneMath

First note, log(1+sqrt(x)) does not equal log(1) + log (sqrt(x)). You're thinking about this property:

log(ab) = log(a) + log(b). So, what you should have is this mess below:

$y = \ln{(1+\sqrt{x})} - \ln{x^3}$

On the first part, use the chain rule, on the second part use the chain rule. Show your work and we'll see where you go astray.

3. Oct 24, 2012

HellRyu

O.K. so I started doing the chain rule for the first one and got:

$$(1/(1 + √x) )(1/(2√x) )$$

Is it right so far?

EDIT: I did the second one and got:

$$(1/(x^{3}) ) (3x^{2} )$$

Last edited: Oct 24, 2012
4. Oct 24, 2012

HellRyu

ok I got used the chain rule and got

$$[(1/2x^{-1/2})/(1 + √x)] - [(3x^2)/(x^3)]$$

then

$$1/[ (2√x) + 2x ] - 3/x$$

How do I go from here to get the answer :

$$(-6 -5√x)/[2x(1 + √x) ]$$ ?

5. Oct 24, 2012

SammyS

Staff Emeritus
Find a common denominator & combine fractions.