Derivative of cubed root of x with limits

Limits, differentiation, related rates, integration, trig integrals, etc.
Andromeda
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Derivative of cubed root of x with limits

Postby Andromeda » Mon Oct 25, 2010 4:59 pm

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.

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stapel_eliz
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Postby stapel_eliz » Mon Oct 25, 2010 5:14 pm

Andromeda wrote: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! :wink:

Andromeda
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Re: Derivative of cubed root of x with limits

Postby Andromeda » Tue Oct 26, 2010 12:02 am

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.

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Martingale
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Re: Derivative of cubed root of x with limits

Postby Martingale » Tue Oct 26, 2010 1:55 am

Andromeda wrote: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
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Re: Derivative of cubed root of x with limits

Postby Andromeda » Tue Oct 26, 2010 4:37 pm

Martingale wrote:
Andromeda wrote: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?

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Martingale
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Re: Derivative of cubed root of x with limits

Postby Martingale » Tue Oct 26, 2010 4:41 pm

Andromeda wrote:
Martingale wrote:
Andromeda wrote: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


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