What is lnx^2?

Okay, here's some information about ln(x²) in Markdown format with the requested links:

ln(x²) represents the natural logarithm of x squared. It's a mathematical function formed by composing the squaring function x² with the <a href="https://www.wikiwhat.page/kavramlar/natural%20logarithm">natural logarithm</a> function, ln(x).

Key Properties and Considerations:

• Domain: The domain of ln(x²) is all real numbers except for x = 0. This is because x² is always non-negative, and the <a href="https://www.wikiwhat.page/kavramlar/natural%20logarithm">natural logarithm</a> is only defined for positive numbers. Zero is not in the domain of the <a href="https://www.wikiwhat.page/kavramlar/natural%20logarithm">natural logarithm</a>.

• Relationship to 2ln(x): While it might seem like ln(x²) = 2ln(x), this is only true for positive values of x. 2ln(x) is only defined for x > 0, whereas ln(x²) is defined for all non-zero x.

• Even Function: ln(x²) is an <a href="https://www.wikiwhat.page/kavramlar/even%20function">even function</a>. This means that ln((-x)²) = ln(x²). This symmetry reflects about the y-axis.

• Rewriting the Function: A more accurate way to relate ln(x²) to ln(x) involves the absolute value: ln(x²) = 2ln(|x|) for x ≠ 0.

• Differentiation: The derivative of ln(x²) is 2/x for x ≠ 0. This can be found using the <a href="https://www.wikiwhat.page/kavramlar/chain%20rule">chain rule</a>.

• Graph: The graph of ln(x²) is symmetric about the y-axis and has a <a href="https://www.wikiwhat.page/kavramlar/vertical%20asymptote">vertical asymptote</a> at x = 0.