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Logarithmic differentiation

Other ways to differentiate

Concept 11 of 17 in Continuity and Differentiability

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Think about this

For y=xsin⁡xy = x^{\sin x}, the power rule gives sin⁡x⋅xsin⁡x−1\sin x\cdot x^{\sin x - 1}. The exponential rule gives xsin⁡xlog⁡x⋅cos⁡xx^{\sin x}\log x\cdot\cos x. Which one is right?