Question Detail
Question
Find the derivative of y = e2x ln(x + 6)
Correct Answer
Option D is the correct answer.
Detailed Explanation
This requires the product rule: (uv)' = u'v + uv'.Let u = e2x and v = ln(x + 6).Find the derivatives of u and v:u' = d/dx (e2x) = e2x * (2) = 2e2xv' = d/dx (ln(x + 6)) = (1/(x + 6)) * (1) = 1/(x + 6)Now apply the product rule:dy/dx = u'v + uv'dy/dx = (2e2x) * ln(x + 6) + (e2x) * (1/(x + 6))dy/dx = 2e2xln(x + 6) + e2x/(x + 6).This matches option D.
Hint
Use the product rule for differentiation: (uv)' = u'v + uv'.