# First Principle of Derivative and Power Rule

• Apr 29th 2013, 05:05 AM
choi105
First Principle of Derivative and Power Rule
using the first principle of differentiation, find the first derivatives of

f(x) = 3/x2 and 1/(sqrt x)3

- if using product rule i know, but if using first principle, my ans not the same. Please help me.
• Apr 29th 2013, 05:15 AM
a tutor
Re: First Principle of Derivative and Power Rule
How far can you get? Do you know what you are trying to find the limit of?
• Apr 29th 2013, 06:17 AM
dokrbb
Re: First Principle of Derivative and Power Rule
Did you hear about this formula $\displaystyle \frac{dy}{dx} = lim_{h\rightarrow 0} \frac{f(x+h)−f(x)}{h}$

This is called differentiation from first principles, (or the delta method). It gives the instantaneous rate of change of y with respect to x,

dokrbb
• Apr 29th 2013, 06:25 AM
Plato
Re: First Principle of Derivative and Power Rule
Quote:

Originally Posted by choi105
using the first principle of differentiation, find the first derivatives of

f(x) = 3/x2 and 1/(sqrt x)3

- if using product rule i know, but if using first principle, my ans not the same. Please help me.

Both of these (I assume there are two) are really simple algebra.

Can you simply $\displaystyle \frac{\dfrac{3}{(x+h)^2}-\dfrac{3}{x^2}}{h}~?$
• Apr 29th 2013, 06:27 AM
dokrbb
Re: First Principle of Derivative and Power Rule
Quote:

Originally Posted by Plato
Both of these (I assume there are two) are really simple algebra.

Can you simply $\displaystyle \frac{\dfrac{3}{(x+h)^2}-\dfrac{3}{x^2}}{h}~?$

Plato, congrats, you have got 700 thanks ;), a nice number... which I would quickly transform into a prime :)