General question, which formula to use to find derivative?

[theothersophie]

Hi this is my first post ever in MHB, and I'm in Calculus 1 wondering which formula to use to find derivatives. There are 2 as far as I know:

(1)

and the one one at the beginning of this:

(2)

Example Problem:

How would i know which formula to use? Is there a particular reason the example used (2)?

Thanks all. This is a quick post so I'm sorry if I'm unaware of the rules here, you can point me in the right direction to unerstand formatting and rules around MHB.

 

[Ackbach]

Experience is the only teacher as to which formula to use. For example, if $f(x)=x^n$, then using
$$f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$
requires you to use the Binomial Theorem to expand out $(x+h)^n$ satisfactorily. On the other hand, if you use
$$f'(x)=\lim_{y\to x}\frac{f(y)-f(x)}{y-x},$$
then you must factor $y^n-x^n$ to get the factor $y-x$ to cancel. Different students might find the one or the other more difficult or harder to implement. Bottom line: try both, and see which one works out easier.