The Derivative of ex
ex
To find derivate of ex.
limh→0=e(x+h)−exh=limh→0ex.eh−exh
= limh→0ex(eh−1)h
Expansion of eh=1+h+12h2+16h3+.....
∴(eh−1h)=(1+h+12h2+....)−1h
= hh+12h+16h2+....
as h→0=(eh−1h)→1+0+0+....
∴limh→0ex(eh−1)h=ex(1)=ex
∴f′(x)=ex where f(x)=ex.