Let y = x^(sin x) for x > 0. Take logarithms and differentiate to find dy/dx at x = π/2.

Step 1. Logarithms. $\ln y = \sin x\ln x$.

Step 2. Differentiate. $\dfrac{y'}{y} = \cos x\ln x + \dfrac{\sin x}{x}$.

Step 3. Put in $x = \dfrac{\pi}{2}$. $y = \dfrac{\pi}{2}$ and $\dfrac{y'}{y} = 0 + \dfrac{1}{\pi/2} = \dfrac{2}{\pi}$.

Step 4. Multiply. $y' = \dfrac{\pi}{2} \times \dfrac{2}{\pi} = 1$.