What is the Derivative of e^3

The derivative of e cube is zero. Note that e cube is written as e³. In this post, we will learn how to find the derivative of e³.

Derivative of e³ Formula

The formula for the derivative of e³ is 0. This formula is written below.

$\dfrac{d}{dx}(e^3)=0$ or $(e^3)’=0$.

Here, the prime $’$ denotes the first-order derivative.

What is the Derivative of e³?

Answer: The derivative of e³ is 0.

Explanation:

It is known that the value of $e$ is given by the following convergent series:

$e=\sum_{n=0}^\infty$ $=1+\dfrac{1}{1!}+\dfrac{1}{2!}+\cdots$

The number e is irrational, and its value is approximately equal to 2.7182818 (up to 7 decimal places). As e is a fixed number, we conclude that e is a constant.

This implies that e³ is a constant with respect to x.

$\therefore \dfrac{d}{dx}(e^3)=0$ by the rule Derivative of a constant is 0.

Thus, the derivative of e³ is equal to 0.

Also Read: 

Derivative of e²

Derivative of e^2x

Derivative of e^3x

Derivative of log(3x)

Derivative of e³ by First Principle

Let f(x)=e³. Note that e³ is independent of x, so we have f(x+h)=e³ for any values of x and h. By the first principle, the derivative of f(x)=e³ is equal to

$\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$

So $\dfrac{d}{dx}(e^3)$ $=\lim\limits_{h \to 0} \dfrac{e^3-e^3}{h}$

$=\lim\limits_{h \to 0} \dfrac{0}{h}$

$=\lim\limits_{h \to 0} 0$

$=0$.

Hence, the derivative of e³ by the limit definition is equal to 0.

Also Read:

Derivative of log(sin x)

Derivative of log(cos x)

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