To determine whether the statement [tex]\(\frac{d}{d x}(\ln (10)) = \frac{1}{10}\)[/tex] is true or false, let's consider what [tex]\(\ln(10)\)[/tex] represents and how differentiation works.
1. Understanding the Function:
[tex]\(\ln(10)\)[/tex] is the natural logarithm of the constant [tex]\(10\)[/tex]. This is a fixed value and does not depend on the variable [tex]\(x\)[/tex].
2. Differentiation of a Constant:
When we differentiate a constant with respect to a variable [tex]\(x\)[/tex], the result is always zero. This is because a constant does not change, so its rate of change (or derivative) is zero.
3. Step-by-Step Solution:
- The expression [tex]\(\ln(10)\)[/tex] is a constant.
- The derivative of any constant [tex]\(C\)[/tex] with respect to [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
- Therefore, [tex]\(\frac{d}{d x}(\ln(10)) = 0\)[/tex].
However, the statement given is [tex]\(\frac{d}{d x}(\ln(10)) = \frac{1}{10}\)[/tex], which suggests that the derivative of [tex]\(\ln(10)\)[/tex] is [tex]\(\frac{1}{10}\)[/tex].
This is incorrect because the derivative of a constant should be zero, not [tex]\(\frac{1}{10}\)[/tex].
Thus, the statement is False.
