# Rules of Differentiation: Derivative of *e* and
natural logarithm

### Erin Horst

Now that we have explored derivatives, we can now progress
to the rules of differentiation. These rules are simply formulas
that instruct the learner how to compute derivatives depending
on a given function.

The rule for the exponential function, *e*, is by far
one of the easiest differentiation rules to remember. The rule
is

This says that the derivative of the exponential function is
itself. That is, the slope of the tangent line to the exponential
function at a point *a*, is equal to the y-coordinate at
the point *a*.

The rule for the natural logarithmic furnction, ln, is also
an easy derivative to recall. The rule is

This says that the derivative of the natural logarithm is the
function *1/x*. Below are some illustrations of above stated
differentiation rules.

The following graph illustrates the function y=ln(4x) and its
derivative y'=1/x.

The following graph illustrates the function
and its derivative

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