# Thread: First Principle of Derivative and Power Rule

1. ## 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.

2. ## 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?

3. ## Re: First Principle of Derivative and Power Rule

Did you hear about this formula $\frac{dy}{dx} = lim_{h\rightarrow 0} \frac{f(x+h)−f(x)}{h}$

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

4. ## Re: First Principle of Derivative and Power Rule

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

5. ## Re: First Principle of Derivative and Power Rule

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

Can you simply $\frac{\dfrac{3}{(x+h)^2}-\dfrac{3}{x^2}}{h}~?$
Plato, congrats, you have got 700 thanks , a nice number... which I would quickly transform into a prime