Finding derivatives of exponential functions is very easy
We know that exponential functions have highly increasing or decreasing nature. They are in the form of b^{x}. The standard one is of the form e^{x }where e is an exponential constant with value 2.718. This functions are different from the power functions because power functions have the variable in the base and the constant in power whereas it's a reverse case here. Now let us learn deriving exponential functions. The derivative of exponential functions can be founded out by the limit formula. So let us find the derivative of exponential function b^{x}.
As given above, derivative of an exponential function b^{x} comes to be b^{x} ln b, where ln b is the natural log of b i.e. with base e. So if we have the standard function e^{x}, the solution will be e^{x} ln e. But as we know ln e = 1. So the derivatives of exponential functions of the form e^{x} comes to be e^{x} itself.
Lets have derivatives of exponential functions examples
We have learned taking derivatives of exponential functions. So lets have a look at derivatives of exponential functions examples to get the knowledge of the topic thoroughly.
(1) Find the derivative of 4^{x}:
We know that derivative of a^{x} is a^{x} ln a. Here a = 4. So we have the derivative as 4^{x} ln 4.
(2) Find the derivation for e^{2x}:
We have the derivative for e^{x} as e^{x}. There is a power of 2x in our example so we also need to find its derivative which comes to be 2. So the answer will be 2e^{2x}.
Thus we have learned some of the examples. It's time to learn derivatives of exponential functions rules.
Some of the common derivatives of exponential functions rules
Some of the rules for finding derivatives of exponential functions are given below.

Any given exponential function can be derived as the function itself multiplied by natural log of the base and derivative of the power.

The derivative of b^{x} is b^{x} ln b.

The derivative of e^{x} is also e^{x}.
Understanding this rules is enough for learning derivative exponential function.
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