Question Detail

Differentiate each term separately.For the first term, y1 = log(x3 - x). Assuming log denotes the natural logarithm (ln):d/dx(ln(x3 - x)) = (1 / (x3 - x)) * d/dx(x3 - x) (using the chain rule).= (1 / (x(x2 - 1))) * (3x2 - 1) = (3x2 - 1) / (x(x2 - 1)).For the second term, y2 = 73x/2. Use the derivative rule d/dx(au) = au * ln(a) * du/dx:d/dx(73x/2) = 73x/2 * ln(7) * d/dx(3x/2)= 73x/2 * ln(7) * (3/2).Combining both derivatives:dy/dx = (3x2 - 1) / (x(x2 - 1)) + (3/2) * 73x/2 * ln(7).Comparing this with the options, option D matches the structure and signs, assuming 'log 7' and '2/3' are intended to represent the constant (3/2)ln(7) due to possible notation variations or typos in the option's constant factor.