how do I find the derivative of the square root of x

Question

shamil98 · Answer

power rule.
√x = x^1/2
f(x) = x^1/2
f'(x) = x^-1/2

anonymous · Answer

^ you forgot something

f(x) = x^n
f'(x) = nx^(n-1)

So f'(x) in this case would be (1/2)x^(-1/2)

shamil98 · Answer

oh yeah mb

anonymous · Answer

okay.. I guess I'm trying to do it the long way by taking the lim as h approaches 0 but ill do it like this

anonymous · Answer

thank you

wolf1728 · Answer

The derivative of sqrt(x) or x^1/2 =
1/2•(x)•^-1/2•1
The 1 comes from the derivative of x

anonymous · Answer

I don't really see how limits are necessary here... $$\sqrt{x}$$ is the same as$$x ^{1/2}$$
and then you can just differentiate that easily.

shamil98 · Answer

the definition of a derivative, i think that's what the person was using.

shamil98 · Answer

instead of using the rules.

wolf1728 · Answer

I think I'm right. Here's a page of my website: http://1728.org/chainrul.htm Scroll down to the bottom to see the derivative of a square root.

anonymous · Answer

yeah its way easier but this whole section they use lim so I figured I should too but thanks, I understand it :)

anonymous · Answer

Chain rule isn't necessary here, bro @wolf1728  . It's just x to the power of 0.5 There's no inside/outside functions. It's just x^0.5

wolf1728 · Answer

Okay, anyway that derivative has been on my website for years and nobody has told me it's wrong.  (although I could be).

anonymous · Answer

I'm not saying it's wrong, the chain rule still works, but it's not necessary. You're just multiplying the whole thing by 1 which doesn't change it. It would be necessary for eg (x^3)^1/2 or (x^2 + 8x)^1/2, formulas where multiple terms are square rooted but for a single term x^1/2 it won't change anything.

anonymous · Answer

Also @wolf1728  while I'm here, the Google+ link on your website doesn't direct to your profile, just the user's dashboard.

wolf1728 · Answer

okay mentallychallenged I agree. Just thought I'd offer another solution.