simple derivative Q: differentiate sqrt[3x - 1] using def.

[gopher]

I am trying to find the derivative of \(\displaystyle sqrt{3x - 1}\) from the definition. I multiplied by the conjugate and simplified and got:

\(\displaystyle \frac{3h}{h(sqrt{3(x+h)-1}+sqrt{3x-1})}\)

I'm not sure where to take it from here. Any ideas?

 

[galactus]

You have it. Cancel the h's, then you have:

\(\displaystyle \L\\\lim_{x\to\0}\frac{3}{\sqrt{3(x+h)-1}+\sqrt{3x-1}}\)

Now, as h tends to 0, what do you have?. I bet it's the derivative of \(\displaystyle \sqrt{3x-1}\)