How to differentiate y=x^n using the first principle. in this question, i cannot use the rule of differentiation. i have to do the old fashioned way. how do i do it?

By first principles, the derivative is

Use the binomial theorem to expand the numerator:

where

The first term is eliminated, and the limit is

A power of in every term of the numerator cancels with in the denominator:

Finally, each term containing approaches 0 as , and the derivative is

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: