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प्रश्न
What is \[\frac{dy}{dx}\] for \[y=x^{\sin x}\], \[x>0\]?
विकल्प
\[x^{\sin x}\left[\frac{\cos x}{x}+\sin x\log x\right]\]
\[x^{\cos x}\left[\frac{\sin x}{x}+\cos x\log x\right]\]
\[x^{\sin x}\left[\frac{\sin x}{x}+\cos x\log x\right]\]
\[x^{\sin x}\left[\sin x+x\cos x\log x\right]\]
MCQ
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उत्तर
Differentiate \[\sin x\log x\] by the product rule. This gives \[\frac{\sin x}{x}+\cos x\log x\], which is then multiplied by \[y=x^{\sin x}\].
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