Question

If $y=x$ln $x$, then what is the value of $\frac{dy}{dx}$ at $x=1$?

• A. $1$
• B. $1-e$
• C. $1+2e$
• D. None of the above

Answer 1

The correct option is A $1$

The given information is:

$y=x\ln x$

Differentiating once w.r.t to x we get,

$\Rightarrow \frac{dy}{dx}=\ln x+x\times \frac{1}{x}$

$\Rightarrow \frac{dy}{dx}=\ln x+1$

The value of the derivative at x =1 is:

$\Rightarrow y^{\prime }\left(1\right)=\ln 1+1$

$\Rightarrow y^{\prime }\left(1\right)=1$ .....Answer