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Derivative of xˣ

MediumCalculus~4m

Let y=xxy = x^x for x>0x>0. Evaluate dydx\dfrac{dy}{dx} at x=2x = 2. (to 4 decimals)

Show hints (2)+
  1. Logarithmic differentiation: take ln⁡\ln of both sides first.
  2. y′=xx(ln⁡x+1)y' = x^x(\ln x + 1); evaluate at x=2x=2 with 22=42^2=4.

Answer

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6.7726 (± 0.001)

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