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