Finding the unit tangent, unit normal, and the unit binormal vectors to a helix (calculus 3)

Here's a quick Calculus 3 tutorial on finding the unit tangent vector, unit normal vector, and the unit binormal vector of a helix (3sin(t))i+(3cos(t))j+4tk.
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[@duckyoutube6318]

Im pretty new to calculus and i have a question if anyone would care to help me.
I know how to find the derivative of sqrt(x) by using the power rule.
f'(x)=1/2sqrt(x)
But how do i find it using the limit definition? Is the following correct....
Lim h->0 f(x)=sqrt(x)
Lim h->0 f(x+h)-f(x)/h
Lim h->0 f(sqrt(x+h))-f(sqrt(x))/h
Is that correct? Am i to assume that both x and h are roots?
Or would it be better to look at it like this...
lim h->0 f(x+h)^1/2-f(x)^1/2
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h

[@duckyoutube6318]

As i was sitting here i just realized why dont i just try it on paper and see if it fits the answer that the power rule says it is....
Im not smart at all.

[@davidcroft95]

Maybe I'm late for this, but try to "rationalize" the denominator: the difference of square to cancel the two square-roots. After that it's just algebra. Hope this helps :)

[@souysf9926]

Analysis and calculus IS it thé same ??

[@crispeto_2767]

Always has been... (Linear algebra is everywhere)

[@urluberlu2757]

🤩👍

[@eswyatt]

Your'e also teaching us how to make videos by setting them up for editing but not actually editing!

[@Ynook]

I was wondering about that part too. He took a long pause, then he redid the explanation. :))) Maybe he forgot to cut that part out.

[@eswyatt]

​@Ynook He's done it in other vids. I like the rawness