Question

What is the derivative of \[f\left( x \right) = 5\]?

Answer 1

Hint: Derivatives are defined as the varying rate of change of a function with respect to an independent variable. Here, we are given the function and we need to find the derivative of that function. We can find the derivative using definition or simply by using the derivative of x with respect to y. As we know, the derivative of a constant is zero. Thus, by using either of these ways, we will get the final output.

Complete step-by-step answer:
Given that,
\[f\left( x \right) = 5\]
So, we will use derivative of x with respect to y, and we will get,
\[ = \dfrac{d}{{dx}}[f(x)]\]
Substituting the value of the given function, we will get,
\[ = \dfrac{d}{{dx}}[5]\]
We know that, the derivative of a constant is 0 and so applying this, we will get,
\[ = 0\]
Hence, the derivative of \[f\left( x \right) = 5\] is 0.
So, the correct answer is “0”.

Note: The derivative is used to measure the sensitivity of one variable (dependent variable) with respect to another variable (independent variable). It helps to investigate the moment by moment nature of an amount. The process of finding the derivative is called differentiation. The inverse process is called anti-differentiation. If an infinitesimal change in x is denoted as dx, then the derivative of y with respect to x is written as \[\dfrac{{dy}}{{dx}}\].