Read the two statements and choose the correct option.

I. Logarithmic differentiation is needed for $y = x^{x}$, where both the base and the power vary.

II. $\frac{d}{dx} x^{n} = nx^{n - 1}$ applies to $x^{x}$ with $n = x$.

Explanation

1. 01

   I is true: neither the power rule nor the rule for $a^{x}$ covers a varying base and power together.

2. 02

   II is false: $nx^{n - 1}$ needs a constant $n$; it would give $x \cdot x^{x - 1} = x^{x}$, missing the $\log x$ term.