Question Detail

To differentiate y = log(x3 - x) + 73x, we differentiate each term separately.For the first term, log(x3 - x), assuming log means natural logarithm (ln):Let u = x3 - x. Then u' = 3x2 - 1.The derivative of ln(u) is u'/u. So, d/dx(log(x3 - x)) = (3x2 - 1) / (x3 - x) = (3x2 - 1) / (x(x2 - 1)).For the second term, 73x:The derivative of akx is k * akx * ln(a). Here, a = 7 and k = 3.So, d/dx(73x) = 3 * 73x * ln(7).Combining these, dy/dx = (3x2 - 1) / (x(x2 - 1)) + 3 * 73x * ln(7).Comparing this with the given options, option D matches the first term correctly. Although the second term's coefficient (2/3log7) is unusual compared to standard differentiation rules (3ln7), it is the selected option and the first part is correct.