How To Understand Derivatives: The Quotient Rule, Exponents, and Logarithms

Kalid,

Thanks for the intuitive approach. I have the same doubt as Alisa has asked, but i could not find a reply to this post can you please help clarify the below question

This comes up in the quotient rule explanation
"And the difference between “neighbors” (like 1/3 and 1/4) will be 1 / common denominator, aka 1 / (x * (x + 1)). See if you can work out why!"

you seem to have used 1 as the delta variation, I am trying to use dg [a very small diff]
1/(g+dg) - 1/g
= (g-g+dg) / (g^2+gdg)
= -dg / (g^2 + g
dg)

now if dg tends to zero even the numerator tends to zero, what rule do you apply in such case.
i.e. lim dg->0 {-dg/g^2 +g*dg} ==0