Question

What is the derivative of $\pi \left( x \right)$?

Answer 1

From the question given, we have been asked to find the derivative of $\pi \left( x \right)$. To solve this question, we have to know the basic concepts of differentiation. To solve this question, we have to know about differentiation. First, we have to make sure that $\pi$ is a number and we have the $\pi \left( x \right)$ with respect to $x$.

Complete step by step answer:
Let us define differentiation. We can say that differentiation is a method of finding the derivative of a function. It is used to measure the change in one variable, which is a dependent one, with respect to per unit change in another variable, which is an independent one. We also know that a derivative is a function which measures the slope.
From the question we have been given $\pi \left( x \right)$.
Now, to find the derivative of $\pi \left( x \right)$.
We know that $\pi$ is a constant and it is an irrational number.
We should not get confused with the symbol $\pi$. The symbol $\pi$ is just a number and we know that it is roughly equivalent to $3.14$. So, to make it easier to understand, we can replace $\pi$ with $3.14$. Doing this, we will be sure that we are taking the derivative of $3.14x$.
So, first we will keep the constant as it is and then we will multiply it by the derivative of x.
We can find the result using the power rule. It is given by $\dfrac{d}{dx} {{x}^{n}}=n{x}^{n-1}$
Here, we have n as 1. So, we can write it as
$\dfrac{d}{dx}\pi {{x}^{1}}$
Applying the rule, we get
$\Rightarrow \pi {{x}^{1-1}}$
$\Rightarrow \pi {{x}^{0}}$
Since we know that any number (except $0$) to the power zero is $1$, we can write the result as
$\Rightarrow \pi$

Therefore, the derivative of $\pi \left( x \right)$ is $\pi$.

Note: Students should be well known about the concept of differentiation. Students should be well known about the concept and the formulas in differentiation. Students should be very careful while doing the calculation part in the differentiation. One has to make sure that $\pi$ is a number of values $3.14$ and continue the process. We can also recall that the derivative of a constant times $x$ is the constant. We can say this because $\pi x$ represents a linear equation with a constant slope. From the definition, we know that a derivative is the slope and a linear equation has a constant derivative.