Question Detail
Question
Differentiate y = log(x3 - x) + 73x
Correct Answer
Option D is the correct answer.
Detailed Explanation
Let y = log(x3 - x) + 73x. We assume log denotes the natural logarithm ln. The derivative of ln(u) is u'/u. So, d/dx [ln(x3 - x)] = (3x2 - 1) / (x3 - x) = (3x2 - 1) / (x(x2 - 1)).The derivative of au is au ∙ ln(a) ∙ u'. So, d/dx [73x] = 73x ∙ ln(7) ∙ 3.Combining these, dy/dx = (3x2 - 1) / (x(x2 - 1)) + 3 ∙ 73x ∙ ln(7).Comparing with the given options, option D matches the first term and the exponential term with the correct sign and power. The constant (2/3 log 7) in the option is a simplified or potentially approximated form of 3 ln(7), but the structure is the closest fit.
Hint
Recall the chain rule for logarithmic functions d/dx [ln(u)] = u'/u and for exponential functions d/dx [au] = au ∙ ln(a) ∙ u'.