NDA 2017 Maths · Mathematics · Derivatives · medium

The value of d/dx(x^x at x=1 is

Single correct option

The value of

\dfrac{d}{dx}\left(x^x\right)

x=1

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Answer: (D) $1$

Let

y=x^x

, so

\ln y=x\ln x

and

y'=x^x(\ln x+1)

. At

x=1

this is

1\cdot(0+1)=1

. Using the power rule

x\cdot x^{x-1}

alone gives

1

by coincidence at this point but is wrong in general;

0

treats

x^x

as a constant power.

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