Question

Y=e^x differentiate using the first principle

Answer 1

do you mean the limit of the difference quotient? There are several good discussion of the topic online. Google is your friend.

Answer 2

I mean find dy/dx of dat question using d first priniciple

Answer 3

y (x+h) = e^(x+h) = e^x e^h

y(x+h) - y(x) = e^x e^h - e^x

= e^x (e^h - 1)
so
[y(x+h) - yx) ] / h = e^x [e^h-1]/h

as h ----> 0
e^h ----> 1 + h + h^2/2! + h^3/3! ....
so

as h-->0 e^h -1 -----> h + h^2/2 + h^3/3!...
which is h in the limit
so we have
e^x [ h/h }
which is
e^x
will wonders never cease

Answer 4

It always seems like cheating to use a Taylor Series to prove a derivative...

But nice of you to step in and help. It's clear that google is of no use to someone who cannot spell...