Chapter 12, Problem 1RE

Determine whether each of the following statements is true or false, and explain why.

1. The derivative of π³ is 3 π².

To determine

To check: Whether the statement “The derivative of ${\pi }^3$ is $3{\pi }^2$” is true or false and explain the reason.

Answer to Problem 1RE

The given statement is false.

Explanation of Solution

The value of $\pi$ is $\frac{22}{7}$, which is a constant.

The constant rule in the rules of derivative states that ‘The derivative of a constant is always zero’.

Thus, the derivative of ${\pi }^3$ is zero.

Calculation:

The derivative of ${\pi }^3$ is computed as follows:

$\begin{array}{c}{D}_x\left({\pi }^3\right)=\frac{d}{dx}\left({\pi }^3\right)\\ =\frac{d}{dx}{\left(\frac{22}{7}\right)}^3\left[\because \pi =\frac{22}{7}\right]\\ =0\left[\because \frac{d}{dx}\left(k\right)=0\right]\end{array}$

Therefore, the derivative of ${\pi }^3$ is not $3{\pi }^2$.

From the above calculation, it can be concluded that the statement “The derivative of ${\pi }^3$ is $3{\pi }^2$” is false.