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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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HomeDerivative[Solved] What is the Derivative of pi/4?
Derivative of Pi/4
Answer: The derivative of pi/4 is 0.
We know that the value of the number `\pi` is approximately equal to 3.1416 (up to `4` decimal places). Also, the number `\pi` is irrational.
Note that the value of `\pi` is determined by the area of a unit circle (that is, a circle of radius 1). As the area of a unit circle is fixed, so we conclude that `\pi` is a fixed number.
`\Rightarrow \pi` is a constant.
`\Rightarrow \pi/4` is a constant.
So `\pi/4` does not change with respect to any variable.
`\therefore d/dx(\pi/4)=0` by the rule Derivative of a constant is 0.
Thus, the derivative of `\pi/4` is equal to `0`.
Let `f(x)=\pi/4`. As both `\pi` and `4` are constants, the quotient `\pi/4` is independent of `x`. Thus, we have
`f(x+h)=\pi/4` for any values of `x` and `h`.
Now, by the first principle, the derivative of `f(x)` is equal to
`d/dx(f(x))` `=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}`
In this formula, we put `f(x)=\pi/4`.
Hence `d/dx(\pi/4)` `=\lim_{h \to 0} \frac{\pi/4 -\pi/4}{h}`
Thus, the derivative of `\pi/4` from the first principle, that is, by the limit definition is equal to `0`.