Question

Can anyone plz post the procedure for finding the derivative of :-

e^ax


by ab inition method?

Answer 1

Derivative by the <i>ab initio</i> (Lat. "from the beginning") method is to find it from first principles, i.e.
df(x)/dx
=Lim h->0 (f(x+h)-f(x))/h
for f(x)=e^ax, we have
Lim h->0 (e^a(x+h) - e^ax)/h
=Lim h->0 (e^ax*e^ah - e^ax)/h
=Lim h->0 e^ax(e^ah-1)/h
=e^ax Lim h->0 (e^ah-1)/h

Try to evaluate the limit, which should turn out to be a.

Answer 2

Can you plz evaluate the limit.

Lim h->0 (e^ah-1)/h


I'm having problems with it. Thanks