𝑑
𝑑
𝑥
[
𝜋
3
]
=

Question

𝑑
𝑑
𝑥
[
𝜋
3
]
=

BlackTom AI · Accepted Answer

We start by clarifying the likely mathematical expression at hand. The prompt shows a derivative notation, which suggests we are taking the derivative with respect to x of a constant value, most plausibly π/3.
Option 1: '1 3 π' appears to denote the constant π/3. While this is a valid constant, the derivative of a constant with respect to x is not the constant itself but zero. Therefore this option incorrectly identifies the derivative as the constant value rather than its rate of change.
Option 2: '1 4 π 4' seems to attempt to express a different constant (likely π/4 or some misformatted fraction). Regardless of the exact constant, since the expression being differentiated does not involve x, its derivative would still be zero. This option fails because it treats the derivative as the constant instead of its zero rate of change.
Option 3: '0' states that the derivative with respect to x of π/3 is zero. This aligns with the fundamental rule that the derivative of any constant is zero, because constants do not change as x changes.
Option 4: '3 π 2' likely corresponds to 3π/2 as a constant value. Like Options 1 and 2, it represents a fixed value, not a rate of change with respect to x, so it is incorrect for a derivative outcome.
In summary, the correct understanding is that differentiating a constant with respect to x yields zero, whereas the other options confuse the constant value with its derivative or misinterpret the derivative operation.

MATH_1225_17255_202501 3.1 Derivatives of Polynomials and Exponential Functions (timed)

𝑑 𝑑 𝑥 [ 𝜋 3 ] =

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