Question

Differentiation of $y=e^x\ln x$ is

• A. $e^x\ln x-\frac{e^x}{x}$
• B. $e^x\ln x+\frac{2e^x}{x}$
• C. $2e^x\ln x+\frac{e^x}{x}$
• D. $e^x\ln x+\frac{e^x}{x}$

Answer 1

The correct option is D $e^x\ln x+\frac{e^x}{x}$

Using the product rule of differentiation
If $y=u.v$, then $\frac{dy}{dx}=u.v^{{}^{\prime }}+v.u^{{}^{\prime }}$
Let $u$ be $\ln x$ and $v$ be $e^x$
$y=e^x\ln x$
$\therefore \frac{dy}{dx}=e^x\ln x+\frac{e^x}{x}$