Question

Let f(x) = square root of (3x), find the derivative using the difference quotient definition. No shortcuts.
I understand how to get it to (3x+3h-3x)/(h(sqrt(3(x+h) + sqrt(3x)) but am having trouble simplifying further. \: Please explain your process, thank you!

Answer 1

does it have any answer on simplifying?
i got the answer but i don't know whether it's correct or not

Answer 2

Yes! The answer provided is 3/(2sqrt(3x))

Answer 3

ummmm let me see...

Answer 4

i am sorry. i cannot get the answer. i only got this \[\frac{ 3 }{ \sqrt{3x}\sqrt{3h+1} }\]
sorry :(

Answer 5

@appleduardo

Answer 6

that's alright, thank you! that's what I've been getting too, this is a tough one.

Answer 7

dunt know whether this may help u http://www.virtualnerd.com/pre-algebra/real-numbers-right-triangles/squares-square-roots/squares-square-roots-properties-definitions/square-root-quotient-property-definition

Answer 8

Oh you're using the Limit Definition for the Derivative?

Answer 9

\[\Large\rm \lim_{h\to0}\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\]And you simplified it to this point?\[\Large\rm \lim_{h\to0}\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}\]

Answer 10

you've done the hard part, the conjugate, now just cancel the h's in the numerator and denominator and then the -3x + 3x in the numerator also cancels

Answer 11

Notice that you have a 3x and -3x in the numerator.
Sorry I jumped ahead too far :(
Was reading the other girls steps.

Answer 12

and now you can plug a 0 in for h and it wont be divide by 0 :)

Answer 13

OHHH I see now!! Thank you!! (: