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] $