Derivative of exponential functions

Euler's number

is one of the central irrational constants in mathematics, like π . Euler’s number has the following important feature. When set as the base number of an exponential function, the derivative of the function is itself.



The e-base logarithm is called the natural logarithm. It is denoted as

Example 1

Example 2

In this case, the exponent has a function 2x, so when we differentiate, remember to multiply by the derivative of the inner function.

Example 3


We use the Euler's number and the natural logarithm and denote

Now we can differentiate

In general, the derivative of an exponential function is

Example 4

Turn on the subtitles if needed