Question

find the derivative of a radical?

Answer 1

ive started but idk if im going in the right direction

Answer 2

i also need to use the limiting process...

Answer 3

rewrite the square root as an exponent
sqrt(x) is x^(1/2)

Answer 4

i know thats simpler, but my teacher she wants us to use the limiting process, which i keep messing up like half way into it... -_-

Answer 5

\[\frac{d x^{n}}{dx}= n x^{n-1}\]

Answer 6

By the limiting process, do you mean using\[\frac{dy}{dx}= \lim_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}\]

Answer 7

If so, multiply top and bottom by the conjugate
\[\frac{ \sqrt{3(x+\Delta x)+9} - \sqrt{3x+9}}{\Delta x} \cdot \frac{\sqrt{3(x+\Delta x)+9}+ \sqrt{3x+9}}{\sqrt{3(x+\Delta x)+9}+ \sqrt{3x+9}}\]