Question Detail
Question
d/dx (3x² cos⁻¹x) =...
Correct Answer
Option A is the correct answer.
Detailed Explanation
To differentiate the product (3x² cos⁻¹x), use the product rule: d/dx(uv) = u'v + uv'.Let u = 3x², so u' = 6x.Let v = cos⁻¹x, so v' = d/dx(cos⁻¹x) = -1 / √(1-x²).Applying the product rule:d/dx(3x² cos⁻¹x) = (6x)(cos⁻¹x) + (3x²)(-1 / √(1-x²))= 6x cos⁻¹x - 3x² / √(1-x²).This matches option A.
Hint
Apply the product rule for differentiation, treating 3x² as one function and cos⁻¹x as another. Remember the derivative of cos⁻¹x.