# Derivative of 1 | Differentiation of 1

The derivative of 1 is zero. Note that 1 can be treated as a constant function. In this blog post, we will learn how to find the derivative of the constant 1 using different methods.

## Derivative of 1 Formula

The natural number 1 is a constant. As the derivative of a constant is 0, we deduce that the derivative of one is zero.

Thus, the formula for the derivative of 1 is as follows:

d/dx(1) = 0 or (1)’ = 0.

## Derivative of 1 by Power Rule

Recall the power rule of derivatives: The derivative of x to the power n is given by the formula:

d/dx(xn) = nxn-1.

To find the derivative of 1, we will follow the below steps described in the table below:

## Derivative of 1 by First Principle

The derivative of a function f(x) by the first principle is determined by the following limit:

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

Step 1: Put f(x) = 1 in the above formula. Note that f(x+h)=1. So the derivative of the constant 1 by the above first principle is

$\dfrac{d}{dx}(1)$ $=\lim\limits_{h \to 0} \dfrac{1-1}{h}$.

Step 2: Simplifying the above, we obtain that

$\dfrac{d}{dx}(1)$ $=\lim\limits_{h \to 0} \dfrac{0}{h}$

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

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

= 0

Final Answer: Thus, we conclude that the derivative of 1 is zero, and this is obtained by the first principle of derivatives.

Video Solution of Derivative of 1 by First Principle:

### Important Notes on Derivative of 1

• 1 is a constant, so its derivative is zero.
• We can write 1=x0. So by power rule, d/dx(1) = d/dx(x0) = 0 x0-1 = 0.
• The derivative of any whole number is zero.

## FAQs on Derivative of 1

Q1: What is the derivative of 1?

Answer: The derivative of 1 is zero.

Q2: What is the derivative of 2?

Answer: The derivative of 2 is zero.

Q3: What is the derivative of a number?

Answer: As any number is a constant and we know that the derivative of a constant is zero, the derivative of any number will be 0.

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