Well, it's all in the title.

Any help is appreciated!

Printable View

- Sep 3rd 2011, 04:33 PMrtblueWhy doesn't the power rule work with exponential functions?
Well, it's all in the title.

Any help is appreciated! - Sep 3rd 2011, 05:10 PMTheChazRe: Why doesn't the power rule work with exponential functions?
No, it's not!

Are you referring to the derivative of a constant power?

If so, why on earth*would they*be the same?!?!

The proof of the power rule (at least for positive integers) relies on the binomial theorem, which doesn't have an obvious connection with an/the exponential function. - Sep 3rd 2011, 06:20 PMSorobanRe: Why doesn't the power rule work with exponential functions?
Hello, rtblue!

The power rule works for a special form: .

The exponential function is a different animal: .

- Sep 3rd 2011, 08:12 PMProve ItRe: Why doesn't the power rule work with exponential functions?
Try differentiating using first principles or some other method you already know of (like the chain rule)...

Maybe have a read of this, then use what you have learnt from here to extend to differentiating using the Chain Rule.

- Sep 3rd 2011, 09:05 PMterrorsquidRe: Why doesn't the power rule work with exponential functions?
- Sep 3rd 2011, 09:23 PMProve ItRe: Why doesn't the power rule work with exponential functions?
- Sep 4th 2011, 06:25 AMHallsofIvyRe: Why doesn't the power rule work with exponential functions?
This is incorrect. is NOT 0 for all h (or even all small h). It is true that if you take the limits of numerator and denominator separately, you get 0 for

**both**but that is true of**all**derivative limits.

Quote:

Doesn't that mean that the limit does not exist?

What am I missing.