If $y=\pi^2$, then $dy/dx=2\pi$
Is this statement true or false? If false, correct the statement.
My answer to this question is false because $y=\pi^2$, there is no variable.
I like to know if my answer is correct, and I would appreciate explanation.
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$\begingroup$You are correct: the statement is false. Since $\pi^2$ is a constant, its derivative with respect to $x$ is $0$. This is no different in principle from the fact that if $y=4=2^2$, then $\frac{dy}{dx}=0$.
The statement illustrates a failure to apply the chain rule: a corrected version would be
$$\frac{d}{dx}\left(\pi^2\right)=2\pi\cdot\frac{d\pi}{dx}=2\pi\cdot 0=0\;.$$
Of course this is doing far more work than is necessary, since we can recognize immediately that $\pi^2$ itself is already a constant and therefore has derivative $0$.
$\endgroup$ $\begingroup$The derivative of any constant is zero. If $\pi$ is a variable, then $\frac{dy}{dx} = 0$, because $y=\pi^2$ is not a function of $x$.
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