๐/๐๐ฅ[๐]
The expression ๐/๐๐ฅ[๐] represents the derivative of a constant value ๐ with respect to the variable ๐ฅ. When
The expression ๐/๐๐ฅ[๐] represents the derivative of a constant value ๐ with respect to the variable ๐ฅ. When you take the derivative of a constant, the result is always zero.
To see why this is the case, we can use the definition of the derivative. The derivative of a function ๐(๐ฅ) is defined as the limit of the difference quotient as the change in ๐ฅ approaches zero:
๐'(๐ฅ) = lim (๐(๐ฅ + ๐) – ๐(๐ฅ))/๐ as ๐โ0.
Now, let’s apply this definition to the constant function ๐:
๐'(๐ฅ) = lim (๐ – ๐)/๐ as ๐โ0.
Since ๐ – ๐ is equal to zero for any value of ๐, the numerator of the difference quotient is always zero:
๐'(๐ฅ) = lim (0)/๐ as ๐โ0.
No matter what value ๐ approaches, the numerator remains zero while the denominator approaches zero. This means that the entire expression approaches zero:
๐'(๐ฅ) = 0.
Therefore, the derivative of a constant ๐ with respect to ๐ฅ is always zero: ๐/๐๐ฅ[๐] = 0.
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