Q16 of 354 Page 11

If y = x^x, find at x = e.

y = x^x

Taking logarithm on both sides,

log y = x log x

Differentiating w.r.t. x on both sides,

=1+log x

=x^x (1+log x)

So, at x = e,

=e^e (1+1)

=2e^e (Ans)

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If and find .

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