Question Detail
Question
Given that \(y = \ln(x^3)+\ln(7x)\), find \(\frac{dy}{dx}\).
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, simplify the expression for (y) using logarithm properties:(y = \ln(x^3) + \ln(7x))(y = 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{dy}{dx} = \frac{4}{x}).
Hint
Simplify the logarithmic expression using \(\ln(ab) = \ln a + \ln b\) and \(\ln(a^b) = b\ln a\) before differentiating.