Question Detail
Question
Find the derivative of y = e^(2x) ln(x + 6)
Correct Answer
Option D is the correct answer.
Detailed Explanation
Use the product rule: (uv)' = u'v + uv'.Let u = e^(2x) and v = ln(x + 6).Then u' = d/dx(e^(2x)) = e^(2x) * 2 = 2e^(2x).And v' = d/dx(ln(x + 6)) = 1 / (x + 6) * 1 = 1 / (x + 6).Applying the product rule:dy/dx = (2e^(2x)) * ln(x + 6) + e^(2x) * (1 / (x + 6))dy/dx = 2e^(2x) ln(x + 6) + e^(2x) / (x + 6).This matches option D when the terms are reordered.
Hint
Apply the product rule for differentiation, remembering the chain rule for e^(2x).