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:
Write 1 as the power of x | 1 = x0 |
Differentiate both sides w.r.t. x | d/dx(1) = d/dx(x0) |
Apply power rule of derivative | d/dx(1) = d/dx(x0) = 0 x0-1 = 0 |
Conclusion: | The derivative of 1 is equal to 0 |
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:
Also Read:
Derivative of 1/x: | -1/x2 |
Derivative of sin 3x: | 3cos 3x |
Derivative of esin x : | cos x esin x |
Derivative of log 3x: | 1/x |
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
Answer: The derivative of 1 is zero.
Answer: The derivative of 2 is zero.
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.