Help with Differentiability question:)

Question

chaise · Answer

Shoot ^_^

maheshmeghwal9 · Answer

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

chaise · Answer

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

maheshmeghwal9 · Answer

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:)

chaise · Answer

Coudn't be too sure. One thing I can offer is separate your exponents.

$$a^{m-n}=\frac{a^m}{a^n}$$

apoorvk · Answer

smooth function:|dw:1337592098414:dw|