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Slope of a product at a special point

EasyCalculus~3m

Let f(x)=x2ln⁡xf(x)=x^2\ln x. What is the slope of ff at x=ex=e? Give a decimal to four places.

Show hints (2)+
  1. Product rule: f′(x)=2xln⁡x+x2⋅1x=2xln⁡x+xf'(x)=2x\ln x + x^2\cdot\tfrac1x = 2x\ln x + x.
  2. At x=ex=e, use ln⁡e=1\ln e = 1: f′(e)=2e+e=3ef'(e)=2e+e=3e.

Answer

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8.1548 (± 0.001)

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