Question

What is the derivative of f(x)=x^(2/3) ?

Answer 1

Just follow the power rule\[\frac{ d }{ dx}x^2 = nx^{n-1}\]

Answer 2

i haven't learned the power rule yet, only the difference quotient

Answer 3

This is what the power rule looks like\[\large \frac{ d }{ dx}x^n = nx^{n-1}\]

Answer 4

how do you use it?

Answer 5

for example x^3 = 3x^(3-1) = 3x^2

Answer 6

@bibby, you mean d/dx (x^n), right ?

Answer 7

lol yeah, fixed that up in the second post

Answer 8

then would it be 2/3x^(-1/3) ?

Answer 9

exactly. You can rewrite \[\large x^{-\frac{1}{3}}\]

Answer 10

1/x^1/3?

Answer 11

where the 2 ? @bibby ?

Answer 12

The whole thing is multiplied by 2/3 @RadEn

Answer 13

would the derivative be 2/3x^(1/3) ?

Answer 14

correct

Answer 15

yeah , it is 2/3 * x^(-1/3) or 2/(3x^(1/3))

Answer 16

And what type of discontinuity would this function be?

Answer 17

would the function represent an infinite discontinuity?

Answer 18

this is what the graph looks like. I can't tell what kind of discontinuity it'd be
http://www.wolframalpha.com/input/?i=2%2F%283x%5E%281%2F3%29%29