What is the Derivative of e^2

The derivative of e square is zero. Note that e square is denoted by e². In this post, we will learn how to find the derivative of e², that is, how to differentiate e square.

Derivative of e² Formula

The formula for the derivative of e² is 0. This formula is written below.

$\dfrac{d}{dx}(e^2)=0$ or $(e^2)’=0$.

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

What is the Derivative of e²?

Answer: The derivative of e² is 0.

Explanation:

We know 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 $e^2$ is a constant with respect to $x$.

$\therefore \dfrac{d}{dx}(e^2)=0$ by the rule Derivative of a constant is 0.

Thus, the derivative of e2 is equal to 0.

Also Read:

Derivative of e^2x

Derivative of e³

Derivative of e^3x

Derivative of log(3x)

Derivative of e² by First Principle

Let f(x)=e². See that e² is independent of x, so we have f(x+h)=e² for any values of x and h. By the first principle, the derivative of f(x) is equal to

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

So $\dfrac{d}{dx}(e^2)$ $=\lim\limits_{h \to 0} \dfrac{e^2-e^2}{h}$

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

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

= 0.

Thus, the derivative of e² by the limit definition is equal to 0.

Also Read:

Derivative of log(sin x)

Derivative of log(cos x)

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