Derivative of cubed root of x with limits

[Andromeda]

I am having trouble finding the derivative of cubed root of x using only limits. I know it is easy to use chain rule but I cannot use that yet.

[stapel_eliz]

I am having trouble finding the derivative of cubed root of x using only limits.

What expression, exactly, are you working with (the cube of the square root? the cube of the fifth root? something else?)? What have you tried so far?

Please be complete. Thank you!

[Andromeda]

I'm sorry, I meant the cube root of x. as in cuberoot(x).

So far a tried finding the derivative with a limit as h approaches 0
lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)]

With this, I always end up with an indeterminate form.

[Martingale]

I'm sorry, I meant the cube root of x. as in cuberoot(x).

So far a tried finding the derivative with a limit as h approaches 0
lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)]

With this, I always end up with an indeterminate form.

use the fact that

[Andromeda]

I'm sorry, I meant the cube root of x. as in cuberoot(x).

So far a tried finding the derivative with a limit as h approaches 0
lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)]

With this, I always end up with an indeterminate form.

use the fact that

How would that work since and are not cubed numbers?

[Martingale]

I'm sorry, I meant the cube root of x. as in cuberoot(x).

So far a tried finding the derivative with a limit as h approaches 0
lim h-->0[(cuberoot(a+h) - cuberoot(a)) / ((a+h) - a)]

With this, I always end up with an indeterminate form.

use the fact that

How would that work since and are not cubed numbers?

let and