Question Detail

First, simplify the expression for $y$ using logarithm properties:$y = \ln(x^3) + \ln(7x) = 3 \ln x + (\ln 7 + \ln x)$.$y = 4 \ln x + \ln 7$.Now, differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(4 \ln x + \ln 7)$.$\frac{dy}{dx} = 4 \cdot \frac{1}{x} + 0 = \frac{4}{x}$.Thus, option B is the correct answer.