Question

If $y=log\left[e^{x}\left(\frac{x-1}{x+2}\right)^{1/2}\right]$, then $\frac{dy}{dx}$ equal to

• A. $7$
• B. $\frac{3}{x-2}$
• C. $\frac{3}{\left(x-1\right)}$
• D. None of these

Answer 1

Answer: (D)

We have, $y=log\left[e^{x}\left(\frac{x-1}{x+2}\right)^{1/2}\right]$
$=log\,e^{x}+\frac{1}{2}\left[log\left(x-1\right)-log\left(x+2\right)\right]$
$=x+\frac{1}{2}\left[log\left(x-1\right)-log\left(x+2\right)\right]$
$\therefore \frac{dy}{dx}=1+\frac{1}{2}\left[\frac{1}{x-1}-\frac{1}{x+2}\right]$
$=1+\frac{3}{2\left(x-1\right)\left(x+2\right)}$