Question

If $y=\log \left[e^x{\left(\frac{x-2}{x+3}\right)}^{3/4}\right],$ then $\frac{dy}{dx}=$

• A. $1+\frac{3}{4}\left(\frac{1}{x-2}+\frac{1}{x+3}\right)$
• B. $1+\frac{3}{4}\left(\frac{1}{x-2}-\frac{1}{x+3}\right)$
• C. $1-\frac{3}{4}\left(\frac{1}{x-2}+\frac{1}{x+3}\right)$
• D. none of these

Answer 1

Answer: (B)

$y=x\log e+\frac{3}{4}\log \left(\frac{x-2}{x+3}\right)$
= $x+\frac{3}{4}\left[\log \left(x-2\right)-\log \left(x-3\right)\right]$
$\frac{dy}{dx}=1+\frac{3}{4}\left[\frac{1}{x-2}-\frac{1}{x+3}\right]$