SOLUTION: if f(x)=(e^x)ln x, then f'(e)=

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Question 389720: if f(x)=(e^x)ln x, then f'(e)=
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If f%28x%29+=+%28e%5Ex%29%28ln+x%29, then by the Product Rule,

f'(x) = %28e%5Ex%29%28ln+x%29+%2B+%28e%5Ex%29%281%2Fx%29 (somehow the parsing system doesn't accept f'(x) so I put it outside)

Replacing x with e,

f'(e) = e%5Ee+%2B+%28e%5Ee%29%281%2Fe%29+=+e%5Ee+%2B+e%5E%28e-1%29