Question Detail
Question
Obtain the first derivative of y = 7x³ tan 3x with respect to x.
Correct Answer
Option D is the correct answer.
Detailed Explanation
This requires the product rule: d/dx (uv) = u'v + uv'.Let u = 7x³ and v = tan 3x.First, find u': u' = d/dx (7x³) = 21x².Next, find v' using the chain rule for tan(3x): v' = d/dx (tan 3x) = sec²(3x) * d/dx(3x) = 3sec²(3x).Now, apply the product rule:dy/dx = u'v + uv' = (21x²)(tan 3x) + (7x³)(3sec²(3x)).dy/dx = 21x² tan 3x + 21x³ sec²(3x).Both options C and D are identical and match this result. We choose D as per the problem's markings.
Hint
Apply the product rule for differentiation (d/dx (uv) = u'v + uv') and remember to use the chain rule for the derivative of tan(3x).