Question

Help with Differentiability question:)

Answer 1

Shoot ^_^

Answer 2

\[f(x)=e^x\]
We have to show that it is differentiable at each point in its domain.

Answer 3

I guess you could do this by the definition of a derivative, however it is a general rule that the integral and derivative of the function e^x is e^x. You can watch this video if you want the proof:

http://www.youtube.com/watch?v=sSE6_fK3mu0

Answer 4

But I am doing this by L.H.D. & R.H.D. method but getting a tough limit in the L.H.D. end as \[\lim_{h \rightarrow 0} [e^{c-h}-e^c]/-h\]
How to do now? Plz help:)

Answer 5

Coudn't be too sure. One thing I can offer is separate your exponents.

\[a^{m-n}=\frac{a^m}{a^n}\]

Answer 6

smooth function: