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 bx. The standard one is of the form ex 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 bx.
As given above, derivative of an exponential function bx comes to be bx ln b, where ln b is the natural log of b i.e. with base e. So if we have the standard function ex, the solution will be ex ln e. But as we know ln e = 1. So the derivatives of exponential functions of the form ex comes to be ex 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 4x:
We know that derivative of ax is ax ln a. Here a = 4. So we have the derivative as 4x ln 4.
(2) Find the derivation for e2x:
We have the derivative for ex as ex. 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 2e2x.
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 bx is bx ln b.
The derivative of ex is also ex.
Understanding this rules is enough for learning derivative exponential function.
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