1. ## Real quick derivative answer and maybe explain?

Yesterday in my calc class I possed a derivative problem to my professor who spent 40 mins on the problem... burned all class and didnt come up with an answer so I ask you if you know.

y=sqrt(x+sqrt(x+sqrt(x)))

written differently y=(x+(x+(x)^(1/2))^(1/2))^(1/2)

Please find the derivative. or atleast explain how so i may attempt and show prof.

2. See attachment--be kijnd to your professor its not a difficult pblm but is not easy in front of group of people

3. Originally Posted by mib7289
Yesterday in my calc class I possed a derivative problem to my professor who spent 40 mins on the problem... burned all class and didnt come up with an answer so I ask you if you know.

y=sqrt(x+sqrt(x+sqrt(x)))

written differently y=(x+(x+(x)^(1/2))^(1/2))^(1/2)

Please find the derivative. or atleast explain how so i may attempt and show prof.
$\displaystyle y = [x + (x + x^{\frac{1}{2}})^{\frac{1}{2}}]^{\frac{1}{2}}$

It's just chain rule. It will get messy but it's not a hard problem

$\displaystyle \frac{1}{2[x + (x + x^{\frac{1}{2}})^{\frac{1}{2}}]^{\frac{1}{2}}} \cdot 1 + \frac{1}{2(x+x^\frac{1}{2})^\frac{1}{2}} \cdot 1 +\frac{1}{2x^{\frac{1}{2}}}$

Pretty sure that's it.

Edit:
Originally Posted by Calculus26
See attachment--
Looks like I may have missed the 3rd term. But I don't think any of the substitution is necessary.

4. Shananay you are correct-- I diiferentiated one term twice I changed the attachment to reflect this

5. Originally Posted by Calculus26
Shananay you are correct-- I diiferentiated one term twice I changed the attachment to reflect this
okay good, I kept looking at it and was confused why the answers differed