Mathematics

The key here is recognizing that $x^x$ isn't a simple power or exponential—it's a variable base raised to a variable exponent. Rewrite it using logarithms: $y = e^{x \ln x}$, which lets you use the chain rule on a familiar form. Once you differentiate, you'll find that $\frac{dy}{dx}$ involves a factor of $x^x$ itself, which makes plugging in $x = \pi/4$ straightforward.

The key here is recognizing that $x^x$ isn't a simple power or exponential—it's a variable base raised to a variable exponent. Rewrite it using logarithms: $y = e^{x \ln x}$, which lets you use the chain rule on a familiar form. Once you differentiate, you'll find that $\frac{dy}{dx}$ involves a factor of $x^x$ itself, which makes plugging in $x = \pi/4$ straightforward.