b) Find 

To find \(\frac{dy}{dx}\) for the function \( y = x^{\sin x} + (\sin x)^x \), we need to differentiate each term separately using the chain rule and logarithmic differentiation. 

1. **Differentiate \( x^{\sin x} \):**

Let \( u = x^{\sin x} \).

Take the natural logarithm of both sides:

\[ \ln u = \ln(x^{\sin x}) \]

Using the properties of logarithms, we get:

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