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Find dy/dx, if y = x^sinx

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Find dy/dx, if y = xsinx

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Given y = xsinx

⇒ log(y) = log(xsinx)

⇒ log(y) = sinx logx

⇒ 1/y dy/dx = sinx/x + cosx logx

⇒ dy/dx = y (sinx/x + cosx logx)

⇒ dy/dx = xsinx (sinx/x + cosxlogx) 

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