Question

If y=x lnx, then $\frac{dy}{dx}$=?

• A. 1 + lnx
• B. lnx
• C. 1
• D. none of these

Answer 1

The correct option is A

1 + lnx

Here u=x, v=ln x
Differentiating both sides w.r.t. 'x', $\frac{dy}{dx}=\frac{d\left[xlnx\right]}{dx}$
Using product rule = $x\frac{d\left(lnx\right)}{dx}+lnx\frac{d\left(x\right)}{dx}=x\frac{1}{x}+lnx.1=1+lnx$