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

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.