Question

If $y=\frac{\ln x}{x}$, then $\frac{dy}{dx}$ will be

• A. $\frac{(1-\ln x)}{x}$
• B. $\frac{(1+\ln x)}{x^2}$
• C. $\frac{(1-\ln x)}{x^2}$
• D. $\frac{(\ln x-1)}{x^2}$

Answer 1

The correct option is C $\frac{(1-\ln x)}{x^2}$

$y=\frac{1-\ln x}{x}\frac{dy}{dx}=\frac{\left(x\frac{d}{dx}\right(\ln x)-\ln x\frac{d}{dx}(x\left)\right)}{x^2}=\frac{\left(x\right(\frac{1}{x})-\ln x)}{x^2}\frac{dy}{dx}=(1-lnx)/x^2$