Question

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

• A. \( 3 + \frac{21}{2(x - 4)(x + 3)} \)
• B. \( 3 + \frac{21}{(x - 4)(x + 3)} \)
• C. \( 3 + \frac{21}{2(x + 3)(x - 4)} \)
• D. \( 3 + \frac{7}{(x - 4)(x + 3)} \)

Hint:

When differentiating logarithmic functions, first simplify the expression using logarithmic properties, then apply the chain rule to differentiate.