Some people write ex as exp(x).
e is an irrational number approximately equal to 2.718282 (to 6 d.p.)
This means that at any point on the graph of the exponential function the gradient of the curve at that point is equal to the value of the function (the y-value) at that point.
The function can also be written as a series.
It can be seen that if this series is differentiated term by term the result is the same series!
If x = 1 then the value of e can be worked out to the required accuracy using the series.
This means that:
If f(x) = ex
then f '(x) = ex
Using the Chain Rule with Exponential Functions
To differentiate functions such as f(x) = e2x the chain rule is used.
example f(x) = e2x
f '(x) = 2. e2x = 2e2x
In general terms:
If f(x) = eax
then f '(x) = aeax
example f(x) = 3e200x
f '(x) =3e200x . 200