Using the chain rule, we have:
$$\frac{d}{d x}\left[x^{\sin x}\right] = \frac{d}{d x}\left[e^{\ln(x^{\sin x})}\right]$$
Now, using the power rule and the chain rule for exponential functions, we get:
$$\frac{d}{d x}\left[e^{\sin x \ln x}\right] = e^{\sin x \ln
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