- #1

sooyong94

- 173

- 2

## Homework Statement

How to I find the derivative of

##y=\sqrt{\sqrt{(1+\sqrt{x})}-1}##

## Homework Equations

Logarithmic derivative

## The Attempt at a Solution

I decided to take natural logs to both sides, and this is what I have:

##\ln y=\frac{1}{2} \ln (\sqrt{(1+\sqrt{x})}-\frac{1}{2}##

##\ln y=\frac{1}{4} \ln(1+\sqrt{x})-\frac{1}{2}##

Then an implicit derivative gave me this:

##\frac{1}{y} \frac{dy}{dx}=\frac{1}{8} (\frac{1}{\sqrt{x}+x})##

Now when I multiply both sides by y, the expression becomes very complicated. How do I manipulate them? :(