Question

What is derivative of $\pi$ divided by 2?

Answer 1

We are asked to find the derivative of $\dfrac{\pi }{2}$ .The symbol $\pi$ is widely used in the formulae of mathematics and physics. It is a mathematical constant and has various equivalent definitions. We start to solve the given question by finding out the value $\dfrac{\pi }{2}$ . Then, we find the derivative of it to get the desired result.

Complete step-by-step solution:
We are given a value of $\dfrac{\pi }{2}$ and need to find the derivative of it. We solve this question using the rules of differentiation.
The number $\pi$ a mathematical constant is a key number that assumes the same value irrespective of the change in other parameters. The symbol $\pi$ is a mathematical constant.
The symbol $\pi$ is used in many formulae in mathematics. It is usually defined as the ratio of the circumference of a circle to its diameter.
It is mathematically given as follows,
$\Rightarrow \pi =\dfrac{C}{d}$
Here,
C is the circumference of the circle
d is the diameter of the circle
The value of $\pi$ is equal to 3.14.
As per the question,
We need to find the value of $\dfrac{\pi }{2}$
$\Rightarrow \dfrac{\pi }{2}$
Substituting the value of $\pi$ in the above expression, we get,
$\Rightarrow \dfrac{\pi }{2}=\dfrac{3.14}{2}$
Simplifying the above equation, we get,
$\therefore \dfrac{\pi }{2}=1.57$
Now, we need to find the derivative of $\dfrac{\pi }{2}$
$\Rightarrow \dfrac{d}{dx}\left( \dfrac{\pi }{2} \right)$
Substituting the value of $\dfrac{\pi }{2}$ , we get,
$\Rightarrow \dfrac{d}{dx}\left( 1.57 \right)$
From the rules of differentiation, the derivative of any constant term is equal to zero.
Let the constant term be c then,
$\Rightarrow \dfrac{d}{dx}\left( c \right)=0$
In our case, the value 1.57 is a constant term.
Following the same, we get,
$\Rightarrow \dfrac{d}{dx}\left( 1.57 \right)=0$
$\therefore$ The derivative of $\dfrac{\pi }{2}$ is zero.

Note: A symbol $\pi$ is an irrational number whose decimal value is infinitely long with no repeating pattern and so it cannot be represented in the form of a fraction. The fraction $\dfrac{22}{7}$ is used to approximately represent $\pi$ but no fraction can express its exact value.